In eukaryotes with separate sexes, sex determination often involves sex chromosomes which have diverged as a consequence of recombination suppression. In species with old heteromorphic sex chromosomes, the non-recombining Y(-W) chromosome is typically highly degraded and has lost most of its genes. However, the dynamics of how and how quickly this degradation occurs remain largely unknown because species with young sex chromosomes, characterised by recent recombination suppression, are understudied. We discovered such young sex chromosomes in the ant cricket Myrmecophilus myrmecophilus, which displays a neo-XY system stemming from an X-autosome fusion. We generated a chromosomal-level assembly of the female genome and compared it to male genomic data. We identified four distinct regions on the X, including two strata with varying degrees of Y chromosome degeneration. Phylogenetic studies and genomic comparisons with closely related species revealed two cases of taxonomic synonymies and that the Myrmecophilus neo-sex chromosomes likely evolved approximately 7 million years ago. The X strata subsequently emerged as a consequence of two localised events of recombination suppression. Ant crickets thus represent a promising new model for studying the early stages of sex chromosome degeneration.