The deubiquitinating enzyme BAP1 is a tumor suppressor, among others involved in cholangiocarcinoma. BAP1 has many proposed molecular targets, while its Drosophila homolog is known to deubiquitinate histone H2AK119. We introduce BAP1 loss-of-function by CRISPR/Cas9 in normal human cholangiocyte organoids. We find that BAP1 controls the expression of junctional and cytoskeleton components by regulating chromatin accessibility. Consequently, we observe loss of multiple epithelial characteristics while motility increases. Importantly, restoring the catalytic activity of BAP1 in the nucleus rescues these cellular and molecular changes. We engineer human liver organoids to combine four common cholangiocarcinoma mutations (TP53, PTEN, SMAD4, and NF1). In this genetic background, BAP1 loss results in acquisition of malignant features upon xenotransplantation. Thus, control of epithelial identity through the regulation of chromatin accessibility appears to be a key aspect of BAP1's tumor suppressor function. Organoid technology combined with CRISPR/Cas9 provides an experimental platform for mechanistic studies of cancer gene function in a human context.