<p>Male-biased offspring sex ratios have been associated with extra-pair mating in some bird species. This has been interpreted as evidence of adaptive sex allocation by females in response to securing sperm from high-quality males. Here, we propose an alternative, non-adaptive hypothesis for a male bias based on mitonuclear compatibility. Some molecular complexes involved in cellular respiration are composed of proteins produced by Z-linked genes and mitochondrial genes. Incompatibility between these proteins can negatively affect viability. Females, having only one Z chromosome (from their father), are especially vulnerable. In situations in which extra-pair sires are less compatible with females than within-pair sires, relatively high mortality among female offspring sired by extra-pair males could skew sex ratios towards males. This is expected when females choose within-pair mates with respect to mitonuclear compatibility, but do not do so with extra-pair sires; we describe several circumstances in which this is plausible. We lay out predictions and required data to test our hypothesis in future studies. We also demonstrate how to test the hypothesis retrospectively, using data from a Northern House Wren (<i>Troglodytes aedon</i>) population in which extra-pair offspring are more likely to be male than female. Consistent with the hypothesis, we found more unhatched eggs in broods with extra-pair young and significant differences in the variance and skewness of extra- and within-pair sex ratios. Further exploration into mitonuclear compatibility as a determinant of offspring sex ratios in this and other species awaits.</p>