Avian egg colour has been explained as mainly serving crypsis or mimetism, although the function of certain colours (e.g. blue and green) has not yet been demonstrated. We interpret egg colour as a sexually selected signal of the laying female's genetic quality to its mate in order to induce a higher allocation of paternal care. The blue–green pigment biliverdin is an antioxidant, the deposition of which may signal antioxidant capacity whereas the deposition of the brown pigment protoporphyrin, a pro-oxidant, may signal tolerance of oxidative stress. Egg ground colour is presumably heritable and phylogenetically labile. The hypothesis can be applied to animals with colourful eggs and paternal care.