The purpose of the study was to test the genetics of individual egg hatchability. Hatching outcome (0,1) of each of the eggs (126,430) laid during hatching seasons of 5 generations of a Rhode Island White population was analyzed with models that attributed the direct additive effect either to an egg or to a hen. A Gibbs sampling procedure, accounting for dichotomous nature of the trait, was employed for variance component estimation. The egg/embryo direct additive component was negligibly small (h(2) = 0.007) from the point of view of the accuracy of the hatchability proof. The hen direct additive component, though more than 12 times higher (h(2) = 0.087) than that of the egg, was still more than 2 times smaller than the component because of her permanent environment (p(2) = 0.221). More accurate definition of hens' environmental needs may prove to be more effective for hatching outcome improvement than increasing the accuracy of the reproduction proof, because current selection has to be performed before the individual hatchability record is known.