The majority of human breast cancers exhibit luminal epithelial differentiation. However, most aggressive behavior, including invasion and purported cancer stem cell activity, are considered characteristics of basal-like cells. We asked the following questions: Must luminal-like breast cancer cells become basal-like to initiate tumors or to invade? Could luminally differentiated cells within a basally initiated hierarchy also be tumorigenic? To answer these questions, we used rare and mutually exclusive lineage markers to isolate subsets of luminal-like and basal-like cells from human breast tumors. We enriched for populations with or without prominent basal-like traits from individual tumors or single cell cloning from cell lines and recovered cells with a luminal-like phenotype. Tumor cells with basal-like traits mimicked phenotypic and functional behavior associated with stem cells assessed by gene expression, mammosphere formation and lineage markers. Luminal-like cells without basal-like traits, surprisingly, were fully capable of initiating invasive tumors in NOD SCID gamma (NSG) mice. In fact, these phenotypically pure luminal-like cells generated larger and more invasive tumors than their basal-like counterparts. The tumorigenicity and invasive potential of the luminal-like cancer cells relied strongly on the expression of the gene GCNT1, which encodes a key glycosyltransferase controlling O-glycan branching. These findings demonstrate that basal-like cells, as defined currently, are not a requirement for breast tumor aggressiveness, and that within a single tumor there are multiple "stem-like" cells with tumorigenic potential casting some doubt on the hypothesis of hierarchical or differentiative loss of tumorigenicity.