This is a Phase III, randomized, multicenter, international, 2-arm, open-label clinical trial designed to compare the safety and efficacy of trastuzumab emtansine (T-DM1) with that of capecitabine + lapatinib in participants with human epidermal growth factor receptor 2 (HER2)-positive locally advanced or metastatic breast cancer. Participants will be treated until disease progression (PD), unmanageable toxicity, or study termination. Once disease progression is reported, all participants will be followed for survival every 3 months until death, loss to follow-up, withdrawal of consent, or study termination.