Some animal groups, such as stick insects (Phasmatodea), have repeatedly evolved alternative reproductive strategies, including parthenogenesis. Genomic studies have found modification of the genes underlying meiosis exists in some of these animals. Here we examine the evolution of copy number, evolutionary rate, and gene expression in candidate meiotic genes of the New Zealand geographic parthenogenetic stick insect Clitarchus hookeri. We characterized 101 genes from a de novo transcriptome assembly from female and male gonads that have homology with meiotic genes from other arthropods. For each gene we determined copy number, the pattern of gene duplication relative to other arthropod orthologs, and the potential for meiosis-specific expression. There are five genes duplicated in C. hookeri, including one also duplicated in the stick insect Timema cristinae, that are not or are uncommonly duplicated in other arthropods. These included two sister chromatid cohesion associated genes (SA2 and SCC2), a recombination gene (HOP1), an RNA-silencing gene (AGO2) and a cell-cycle regulation gene (WEE1). Interestingly, WEE1 and SA2 are also duplicated in the cyclical parthenogenetic aphid Acyrthosiphon pisum and Daphnia duplex, respectively, indicating possible roles in the evolution of reproductive mode. Three of these genes (SA2, SCC2, and WEE1) have one copy displaying gonad-specific expression. All genes, with the exception of WEE1, have significantly different nonsynonymous/synonymous ratios between the gene duplicates, indicative of a shift in evolutionary constraints following duplication. These results suggest that stick insects may have evolved genes with novel functions in gamete production by gene duplication.