Sex chromosomes evolve once recombination is halted between a homologous pair of chromosomes. The dominant model of sex chromosome evolution posits that recombination is suppressed between emerging X and Y chromosomes in order to resolve sexual conflict. Here we test this model using whole genome and transcriptome resequencing data in the guppy, a model for sexual selection with many Y-linked colour traits. We show that although the nascent Y chromosome encompasses nearly half of the linkage group, there has been no perceptible degradation of Y chromosome gene content or activity. Using replicate wild populations with differing levels of sexually antagonistic selection for colour, we also show that sexual selection leads to greater expansion of the non-recombining region and increased Y chromosome divergence. These results provide empirical support for longstanding models of sex chromosome catalysis, and suggest an important role for sexual selection and sexual conflict in genome evolution.