Selection can be a useful way to alter yolk proportion and thereby egg dry matter which, owing to its economic importance, is a trait of substantial importance for the egg-processing industry. However, the egg is primarily the chamber of embryonic development. The main purpose of this study was to estimate genetic correlations between the maternal effect on chick weight at hatching and the direct effect on different egg composition traits, in particular, yolk proportion. Additionally, genetic parameters were estimated for egg composition traits. To create a data set suitable for estimation of genetic parameters, a three-round selection experiment was set up. Birds were selected based on their predicted breeding values for the genetic maternal effect on chick weight and the direct genetic effect on yolk proportion according to the theory of elliptical selection. Genetic parameters were estimated using a multiple trait animal model and restricted maximum likelihood. The maternal heritability for chick weight was 0.5, whereas the direct heritability was dose to 0. The genetic correlations between the maternal effect on chick weight and the direct effect on yolk proportion, yolk weight, albumen weight, albumen dry matter concentration, and egg weight were 0.14, 0.76, 0.93, 0.14, and 0.99, respectively. The heritabilities for yolk proportion, yolk weight, albumen weight, albumen dry matter concentration, and egg weight were 0.33, 0.43, 0.57, 0.38, and 0.60, respectively. We conclude that breeding ought to be a useful way to increase egg dry matter with no expected unfavorable correlated effects on chick weight.