Certain genetic disorders are rare in the general population, but more common in individuals with specific trisomies. Examples of this include leukemia and duodenal atresia in trisomy 21. This paper presents a linkage analysis method for using trisomic individuals to map genes for such traits. It is based on a very general gene-specific dosage model that posits that the trait is caused by specific effects of different alleles at one or a few loci and that duplicate copies of "susceptibility" alleles inherited from the nondisjoining parent give increased likelihood of having the trait. Our mapping method is similar to identity-by-descent-based mapping methods using affected relative pairs and also to methods for mapping recessive traits using inbred individuals by looking for markers with greater than expected homozygosity by descent. In the trisomy case, one would take trisomic individuals and look for markers with greater than expected homozygosity in the chromosomes inherited from the nondisjoining parent. We present statistical methods for performing such a linkage analysis, including a test for linkage to a marker, a method for estimating the distance from the marker to the trait gene, a confidence interval for that distance, and methods for computing power and sample sizes. We also resolve some practical issues involved in implementing the methods, including how to use partially informative markers and how to test candidate genes.