Despite a critical role for tumor-initiating cancer stem cells (CSCs) in breast cancer progression, major questions remain about the properties and signaling pathways essential for their function. Recent discoveries highlighting mechanisms of CSC-resistance to the stress caused by chromosomal instability (CIN) may provide valuable new insight into the underlying forces driving stemness properties. While stress tolerance is a well-known attribute of CSCs, CIN-induced stress is distinctive since levels appear to increase during tumor initiation and metastasis. These dynamic changes in CIN levels may serve as a barrier constraining the effects of non-CSCs and shaping the stemness landscape during the early stages of disease progression. In contrast to most other stresses, CIN can also paradoxically activate pro-tumorigenic antiviral signaling. Though seemingly contradictory, this may indicate that mechanisms of CIN tolerance and pro-tumorigenic inflammatory signaling closely collaborate to define the CSC state. Together, these unique features may form the basis for a critical relationship between CIN and stemness properties.