Aneuploidy results in decreased cellular fitness in many different species and model systems. However, aneuploidy is commonly found in cancer cells and often correlates with aggressive growth and poor prognosis, suggesting that the impact of aneuploidy on cellular fitness is context dependent. The BRG1 (SMARCA4) subunit of the SWI/SNF chromatin remodelling complex is a tumour suppressor that is frequently lost in cancer cells. Here, we used a chromosomally stable cell line to test the effect of BRG1 loss on the evolution of aneuploidy. We find that BRG1 deletion leads to an initial loss of fitness in this cell line that improves over time. The improved fitness correlates with a gain of extra copies of chromosome 18. Notably, changes in pathways that are known to promote tolerance to aneuploidy are evident immediately upon loss of BRG1, providing an environment where karyotype changes associated with a fitness advantage can be explored. At least in some genetic backgrounds, therefore, loss of the SWI/SNF complex can contribute to tumourigenesis through tolerance of aneuploidy.