This research study is a Phase II clinical trial. Phase II clinical trials test the effectiveness of an investigational drug to learn whether the drug works in treating a specific cancer. "Investigational" means that the drug is still being studied and that research doctors are trying to find out more about it-such as the safest dose to use, the side effects it may cause, and if the drug is effective for treating different types of cancer. It also means that the FDA has not approved this drug for use patients undergoing adjuvant treatment for HER2+ breast cancer. Trastuzumab emtansine (T-DM1) is a drug that may stop cancer cells from growing. This drug has been used in other research studies and information from those other research studies suggests that this drug may help to prevent the recurrence of breast cancer in this research study. The use of T-DM1 in this research study is experimental, which means it is not approved by any regulatory authority for the adjuvant treatment of HER2-positive breast cancer. However, it FDA-approved for metastatic HER2-positive breast cancer. T-DM1 has caused cancer cells to die in laboratory studies. In preclinical studies, this drug has prevented or slowed the growth of breast cancer. The breast cancer treatments (paclitaxel and Trastuzumab) used in this study are considered part of standard-of-care regimens in early breast cancer. A standard treatment means that this is a treatment that would be accepted by the majority of the medical community as a suitable treatment for your type of breast cancer. In this research study, the investigators are looking to see if the study drug T-DM1 will have less side effects than traditional HER2-positive breast cancer treatment of trastuzumab and paclitaxel. The investigators are also hoping to learn about the long term benefits and disease-free survival of participants who take the study drug T-DM1 in comparison to those participants to take the combination of trastuzumab and paclitaxel.

If a participant agrees to participate in this study she will be asked to undergo some screening tests or procedures to confirm that she is eligible. Many of these tests and procedures are likely to be part of regular cancer care and may be done even if turns out that she does not take part in this research study. If she has had some of these tests or procedures recently, they may or may not have to be repeated. These tests and procedures will include: a medical history, performance status, assessment of your tumor, blood tests, cardiac tests, pregnancy test and a collection of tumor tissue. If these tests show that she is eligible to participate in the research study, she will begin the study treatment. If she does not meet the eligibility criteria, she will not be able to participate in this research study. Because no one knows which of the study options is best, the participant will be "randomized" into one of the study groups after she has had her breast surgery: Group 1 or Group 2. Randomization means that she is put into a group by chance. Neither the participant nor the research doctor will choose what group she will be in. The participant will have a one in three chance of being placed in any group. Approximately 375 study participants will receive the study drug, while 125 study participants will receive the standard therapy of trastuzumab and paclitaxel. Group 1 participants will receive the study drug T-DM1 every three weeks by IV (intravenous injection) for 17 treatments (total of 51 weeks). Group 2 participants will receive the FDA-approved drugs Paclitaxel and Trastuzumab once per week by IV for 12 weeks. Then beginning week 13, participants will receive Trastuzumab only by IV injection every three weeks for the next 13 treatments. During all cycles the participant will have a physical exam and tumor assessment. The investigators would like to keep track of the participant's medical condition for the next five years after the final dose of study drug. The investigators would like to do this by regular visits every 6 months for 3 years after completion of study treatment, and then once a year for the next two years. The investigators may ask for additional follow-up by phone after completion of these visits. Participants who undergo lumpectomy (breast conserving surgery) need to receive breast radiation therapy to participate in this study. Participants who have undergone a mastectomy may receive chest wall and lymph node radiation (as determined by discussion with their physician). Radiation Therapy will begin after the conclusion of all study paclitaxel doses, and after 12 weeks fo the study drug T-DM1.