Chromosomal inversion polymorphisms are common in animals and plants, and recent models suggest that alternative arrangements spread by capturing different combinations of alleles acting additively or epistatically to favour local adaptation. It is also thought that inversions typically maintain favoured combinations for a long time by suppressing recombination between alternative chromosomal arrangements. Here, we consider patterns of linkage disequilibrium and genetic divergence in an old inversion polymorphism in Drosophila melanogaster (In(3R)Payne) known to be associated with climate change adaptation and a recent invasion event into Australia. We extracted, karyotyped and sequenced whole chromosomes from two Australian populations, so that changes in the arrangement of the alleles between geographically separated tropical and temperate areas could be compared. Chromosome-wide linkage disequilibrium (LD) analysis revealed strong LD within the region spanned by In(3R)Payne. This genomic region also showed strong differentiation between the tropical and the temperate populations, but no differentiation between different karyotypes from the same population, after controlling for chromosomal arrangement. Patterns of differentiation across the chromosome arm and in gene ontologies were enhanced by the presence of the inversion. These data support the notion that inversions are strongly selected by bringing together combinations of genes, but it is still not clear if such combinations act additively or epistatically. Our data suggest that climatic adaptation through inversions can be dynamic, reflecting changes in the relative abundance of different forms of an inversion and ongoing evolution of allelic content within an inversion.