Bacterial pathogens show high levels of chromosomal genetic diversity, but the influence of this diversity on the evolution of antibiotic resistance by plasmid acquisition remains unclear. Here, we address this problem in the context of colistin, a ‘last line of defence’ antibiotic. Using experimental evolution, we show that a plasmid carrying the MCR-1 colistin resistance gene dramatically increases the ability of Escherichia coli to evolve high-level colistin resistance by acquiring mutations in lpxC, an essential chromosomal gene involved in lipopolysaccharide biosynthesis. Crucially, lpxC mutations increase colistin resistance in the presence of the MCR-1 gene, but decrease the resistance of wild-type cells, revealing positive sign epistasis for antibiotic resistance between the chromosomal mutations and a mobile resistance gene. Analysis of public genomic datasets shows that lpxC polymorphisms are common in pathogenic E. coli, including those carrying MCR-1, highlighting the clinical relevance of this interaction. Importantly, lpxC diversity is high in pathogenic E. coli from regions with no history of MCR-1 acquisition, suggesting that pre-existing lpxC polymorphisms potentiated the evolution of high-level colistin resistance by MCR-1 acquisition. More broadly, these findings highlight the importance of standing genetic variation and plasmid/chromosomal interactions in the evolutionary dynamics of antibiotic resistance.