Sex chromosomes have evolved repeatedly across the tree of life and often exhibit extreme size dimorphism due to genetic degeneration of the sex-limited chromosome (e.g. the W chromosome of some birds and Y chromosome of mammals). However, in some lineages, ancient sex-limited chromosomes have escaped degeneration. Here, we study the evolutionary maintenance of sex chromosomes in the ostrich (Struthio camelus), where the W remains 65% the size of the Z chromosome, despite being more than 100 million years old. Using genome-wide resequencing data, we show that the population scaled recombination rate of the pseudoautosomal region (PAR) is higher than similar sized autosomes and is correlated with pedigree-based recombination rate in the heterogametic females, but not homogametic males. Genetic variation within the sex-linked region (SLR) (π = 0.001) was significantly lower than in the PAR, consistent with recombination cessation. Conversely, genetic variation across the PAR (π = 0.0016) was similar to that of autosomes and dependent on local recombination rates, GC content and to a lesser extent, gene density. In particular, the region close to the SLR was as genetically diverse as autosomes, likely due to high recombination rates around the PAR boundary restricting genetic linkage with the SLR to only ~50Kb. The potential for alleles with antagonistic fitness effects in males and females to drive chromosome degeneration is therefore limited. While some regions of the PAR had divergent male-female allele frequencies, suggestive of sexually antagonistic alleles, coalescent simulations showed this was broadly consistent with neutral genetic processes. Our results indicate that the degeneration of the large and ancient sex chromosomes of the ostrich may have been slowed by high recombination in the female PAR, reducing the scope for the accumulation of sexually antagonistic variation to generate selection for recombination cessation.