Signalling by the cytokine LIF and its downstream transcription factor, STAT3, prevents differentiation of pluripotent embryonic stem cells (ESCs). This contrasts with most cell types where STAT3 signalling induces differentiation. We find that STAT3 binding across the pluripotent genome is dependent on Brg1, the ATPase subunit of a specialized chromatin remodelling complex (esBAF) found in ESCs. Brg1 is required to establish chromatin accessibility at STAT3 binding targets, preparing these sites to respond to LIF signalling. Brg1 deletion leads to rapid polycomb (PcG) binding and H3K27me3-mediated silencing of many Brg1-activated targets genome wide, including the target genes of the LIF signalling pathway. Hence, one crucial role of Brg1 in ESCs involves its ability to potentiate LIF signalling by opposing PcG. Contrary to expectations, Brg1 also facilitates PcG function at classical PcG targets, including all four Hox loci, reinforcing their repression in ESCs. Therefore, esBAF does not simply antagonize PcG. Rather, the two chromatin regulators act both antagonistically and synergistically with the common goal of supporting pluripotency.