Clutch size and egg mass are life history traits that have been extensively studied in wild bird populations, as life history theory predicts a negative trade-off between them, either at the phenotypic or at the genetic level. Here, we analyse the genomic architecture of these heritable traits in a wild great tit (Parus major) population, using three marker-based approaches - chromosome partitioning, quantitative trait locus (QTL) mapping and a genome-wide association study (GWAS). The variance explained by each great tit chromosome scales with predicted chromosome size, no location in the genome contains genome-wide significant QTL, and no individual SNPs are associated with a large proportion of phenotypic variation, all of which may suggest that variation in both traits is due to many loci of small effect, located across the genome. There is no evidence that any regions of the genome contribute significantly to both traits, which combined with a small, nonsignificant negative genetic covariance between the traits, suggests the absence of genetic constraints on the independent evolution of these traits. Our findings support the hypothesis that variation in life history traits in natural populations is likely to be determined by many loci of small effect spread throughout the genome, which are subject to continued input of variation by mutation and migration, although we cannot exclude the possibility of an additional input of major effect genes influencing either trait.