Genome-wide association studies typically evaluate the autosomes and sometimes the X Chromosome, but seldom consider the Y or mitochondrial (MT) Chromosomes. We genotyped the Y and MT Chromosomes in heterogeneous stock (HS) rats (Rattus norvegicus), an outbred population created from 8 inbred strains. We identified 8 distinct Y and 4 distinct MT Chromosomes among the 8 founders. However, only 2 types of each nonrecombinant chromosome were observed in our modern HS rat population (generations 81-97). Despite the relatively large sample size, there were virtually no significant associations for behavioral, physiological, metabolome, or microbiome traits after correcting for multiple comparisons. However, both Y and MT Chromosomes were strongly associated with the expression of a few genes located on those chromosomes, which provided a positive control. Our results suggest that within modern HS rats there are no Y and MT Chromosomes differences that strongly influence behavioral or physiological traits. These results do not address other ancestral Y and MT Chromosomes that do not appear in modern HS rats, nor do they address effects that may exist in other rat populations, or in other species.