This is an international multi-center trial that will enroll patients with locally advanced, unresectable, or metastatic gastric, esophageal, or gastro-esophageal junction cancer whose tumors have amplification of the ErbB2 (HER2) gene. The trial will investigate whether lapatinib, when added to the chemotherapy regimen, capecitabine plus oxaliplatin (CapeOx), extends the time to progression and overall survival. Tumor ErbB2 (HER2) status must be known before trial entry. CapeOx is administered to all patients, and patients will be randomly assigned to receive either lapatinib or placebo.