We analyse the problem of a non-producing patentee who licenses an essential process innovation to a vertical Cournot oligopoly. The vertical oligopoly is composed of an upstream and a downstream sector which may differ in their efficiency or, in other words, in the benefit they derive from the innovation. In this framework we characterise the optimal licensing contract in terms of the licensing revenue maximising policy (fixed-fee or per-unit royalty) and sector (upstream and/or downstream sector). First, it is shown that under a fixed-fee contract licensing to the less efficient industry sector may be the patentee's licensing revenue maximising strategy. Here, licensing to a less efficient downstream market is all the time optimal in terms of consumer surplus and aggregate economic welfare. Conversely, licensing to a less or equally efficient upstream industry is potentially inefficient. Second, our findings reveal that the optimal licensing policy is sector dependent. A per-unit royalty contract may dominate a fixed-fee policy on the downstream market in terms of licensing revenues, while offering a per-unit royalty contract to the upstream industry is never optimal. As a third and final point we address the case of licensing to both industry sectors. Here we also identify conditions under which two-sector licensing of both sectors is less profitable than one-sector licensing of a single industry (and vice versa).