ATEMPT 2.0: Adjuvant T-DM1 vs TH

Inclusion Criteria: * Patients must have HER2-positive Stage I histologically confirmed invasive carcinoma of the breast. Patients must have node-negative (N0) or micrometastases (N1mic) breast cancer according to the AJCC 8th edition anatomic staging table. * If the patient has had a negative sentinel node biopsy, then no further axillary dissection is required, and the patient is determined to be node-negative. If an axillary dissection without sentinel lymph node biopsy is performed to determine nodal status, at least six axillary lymph nodes must be removed and analyzed, and determined to be negative, for the patient to be considered node-negative. Axillary nodes with single cells or tumor clusters ≤ 0.2 mm by either H\&E or immunohistochemistry (IHC) will be considered node-negative. * Any axillary lymph node with tumor clusters between 0.02 and 0.2 cm is considered a micrometastasis. Patients with a micrometastasis are eligible. An axillary dissection is not required to be performed in patients with a micrometastasis found by sentinel node evaluation. In cases where the specific pathologic size of lymph node involvement is subject to interpretation, the principal investigator will make the final determination as to eligibility. The investigator must document approval in the patient medical record. * Patients who have an area of a T1aN0, ER+ (defined as \>10%), HER2-negative cancer in addition to their primary HER2-positive tumor are eligible. * HER2-positive by ASCO CAP 2018 guidelines, confirmed by central testing. NOTE: HER-2 status must be confirmed to be positive by central review by NeoGenomics prior to patient starting protocol therapy. Patients previously having had HER2 immunohistochemical testing by NeoGenomics do not need to undergo retesting for central confirmation of HER2 status. NOTE: DCIS components will not be counted in the determination of HER2 status * ER/PR determination is required. ER and PR assays should be performed by immunohistochemical methods according to the local institution standard protocol. * Bilateral breast cancers that individually meet eligibility criteria are allowed. * Patients with multifocal or multicentric disease are eligible, as long as each tumor individually meets eligibility criteria. Central confirmation is needed for any site of disease that is tested to be HER2-positive by local testing (unless testing was previously done by NeoGenomics). * Patients with a history of ipsilateral DCIS are eligible if they were treated with wide excision alone, without radiation therapy, or treated with a mastectomy for this current breast cancer. Patients with a history of contralateral DCIS are not eligible. * ≤ 90 days between the planned treatment start date and the patient's most recent breast surgery for this breast cancer * ≥ 18 years of age with any menopausal status. * ECOG Performance Status 0 or 1 * All tumor should be removed by either a modified radical mastectomy or a segmental mastectomy (lumpectomy), with either a sentinel node biopsy or axillary dissection * All margins should be clear of invasive cancer or DCIS (i.e. no tumor on ink). The local pathologist must document negative margins of resection in the pathology report. If all other margins are clear, a positive posterior (deep) margin is permitted, provided the surgeon documents that the excision was performed down to the pectoral fascia and all tumor has been removed. Likewise, if all other margins are clear, a positive anterior (superficial; abutting skin) margin is permitted provided the surgeon documents that all tumor has been removed. * Patients undergoing breast conservation therapy (i.e. lumpectomy) must not have any contraindications to radiation therapy. Radiation to the conserved breast is required. * Patients may have received up to 4 weeks of tamoxifen therapy, or other hormonal therapy, for adjuvant therapy for this cancer. Patients cannot receive adjuvant hormonal therapy during protocol treatment for the first 12 weeks. * Prior oophorectomy for cancer prevention is allowed. * Patients who have undergone partial breast radiation (duration ≤ 14 days) prior to registration are eligible. Partial breast radiation must be completed prior to 2 weeks before starting protocol therapy. Patients who have undergone whole breast radiation are not eligible. * Patients who have participated in a window study (treatment with an investigational agent prior to surgery for ≤ 2 weeks) are eligible. Patients must have discontinued the investigational agent at least 14 days before participation. * Adequate bone marrow function: * ANC ≥ 1000/mm3, * Hemoglobin ≥ 9 g/dl * Platelets ≥ 100,000/mm3 * Adequate hepatic function: * Total bilirubin ≤ 1.2mg/dL * AST and ALT ≤ 1.5x Institutional ULN * For patients with Gilbert syndrome, the direct bilirubin should be within the institutional normal range. Serum alkaline phosphatase should be ≤ 1.5x Institutional ULN. * Left ventricular ejection fraction (LVEF) ≥ 50% * Premenopausal patients must have a negative serum or urine pregnancy test, including women who have had a tubal ligation and for women less than 12 months after the onset of menopause. * Women of childbearing potential and men with partners of childbearing potential must be willing to use one highly effective form of nonhormonal contraception or two effective forms of nonhormonal contraception by the patient and/or partner. Contraceptive use must be continued for the duration of the study treatment and for 7 months after the last dose of study treatment. Hormonal birth control methods are not permitted. * Patients should have tumor tissue available, and a tissue block of sufficient size to make 15 slides, which must be sent to DFCI for correlative research. If a tissue block is unavailable, sites may send one H\&E-stained slide and 15 unstained sections of paraffin-embedded tissue on uncharged slides. Slide sections should be 4-5 microns in thickness. It is also acceptable to submit 2 cores from a block of invasive tissue using a 1.2 mm diameter coring tool. If tumor is not available, the investigator must document why tissue is not available in the patient medical record, and that efforts have been made to obtain tissue. * Willing and able to sign informed consent * Must be able to read and understand English in order to participate in the quality of life surveys. If patient does not read and understand English, the patient is still eligible, but cannot participate in the quality of life surveys. Exclusion Criteria: * Any of the following due to teratogenic potential of the study drugs: * Pregnant women * Nursing women * Women of childbearing potential who are unwilling to employ adequate contraception (condoms, diaphragms, IUDs, surgical sterilization, abstinence, etc.). * Men who are unwilling to employ adequate contraception (condoms, surgical sterilization, abstinence, etc.). * Locally advanced tumors at diagnosis, including tumors fixed to the chest wall, peau d'orange, skin ulcerations/nodules, or clinical inflammatory changes (diffuse brawny cutaneous induration with an erysipeloid edge) * Patients with a history of previous invasive breast cancer. * History of prior chemotherapy in the past 5 years. * History of paclitaxel therapy * Patients with active liver disease, for example due to hepatitis B virus, hepatitis C virus, autoimmune hepatic disorder, or sclerosing cholangitis * Individuals with a history of a different malignancy are ineligible except for the following circumstances: * Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. * Individuals with the following cancer are eligible regardless of when they were diagnosed and treated: cervical cancer in situ, and non-melanoma cancer of the skin. * Intercurrent illness including, but not limited to: ongoing or active, unresolved systemic infection, renal failure requiring dialysis, active cardiac disease, prior myocardial infarction (asymptomatic changes on EKG suggestive of old MI is not an exclusion), history of CHF, current use of any therapy specifically for CHF, uncontrolled hypertension, significant psychiatric illness, or other conditions that in the opinion of the investigator limit compliance with study requirements.