Adult polycystic kidney disease (APKD) is a single-gene autosomal dominant genetic disorder leading to end-stage renal disease (ESRD, meaning kidney failure). It is associated with mutations in at least two genes, APKD1 and APKD2, but diagnosis is mostly by ultrasonography. We propose a model for critical illness (CI) insurance and estimate rates of onset of ESRD from APKD using two studies. Other events leading to claims under CI policies are included in the model, which we use to study (a) extra premiums under CI policies if the presence of an APKD mutation is known, and (b) the possible costs arising from adverse selection if this information is unavailable to insurers. The extra premiums are typically very high, but because APKD is rare, the possible cost of adverse selection is low. However, APKD is just one of a significant number of single-gene disorders, and this benign conclusion cannot be assumed to apply to all genetic disorders taken together. Moreover, ignoring known genetic risks in underwriting sets a precedent that could have unintended consequences for the underwriting of nongenetic risks of similar magnitude.