Patients with seemingly the same tumour can respond very differently to treatment. There are strong, well-established effects of somatic mutations on drug efficacy, but there is at-most anecdotal evidence of a germline component to drug response. Here, we report a systematic survey of how inherited germline variants affect drug susceptibility in cancer cell lines. We develop a joint analysis approach that leverages both germline and somatic variants, before applying it to screening data from 993 cell lines and 265 drugs. Surprisingly, we find that the germline contribution to variation in drug susceptibility can be as large or larger than effects due to somatic mutations. Several of the associations identified have a direct relationship to the drug target. Finally, using 17-AAG response as an example, we show how germline effects in combination with transcriptomic data can be leveraged for improved patient stratification and to identify new markers for drug sensitivity.