Chemoresistance is a major obstacle to the treatment of triple‐negative breast cancer (TNBC), which has a poor prognosis. Increasing evidence has demonstrated the essential role of cancer stem cells (CSCs) in the process of TNBC chemoresistance. However, the underlying mechanism remains unclear. In the present study, we report that block of proliferation 1 (BOP1) serves as a key regulator of chemoresistance in TNBC. BOP1 expression was significantly upregulated in chemoresistant TNBC tissues, and high expression of BOP1 correlated with shorter overall survival and relapse‐free survival in patients with TNBC. BOP1 overexpression promoted, while BOP1 downregulation inhibited the drug resistance and CSC‐like phenotype of TNBC cells in vitro and in vivo. Moreover, BOP1 activated Wnt/β‐catenin signaling by increasing the recruitment of cyclic AMP response element‐binding protein (CBP) to β‐catenin, enhancing CBP‐mediated acetylation of β‐catenin, and increasing the transcription of downstream stemness‐related genes CD133 and ALDH1A1. Notably, treating with the β‐catenin/CBP inhibitor PRI‐724 induced an enhancement of chemotherapeutic response of paclitaxel in BOP1‐overexpressing TNBC cells. These findings indicate that BOP1 is involved in chemoresistance development and might serve as a prognostic marker and therapeutic target in TNBC. © 2021 The Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.