Pulsars have at least two impressive applications. First, they can be used as highly accurate clocks, comparable in stability to atomic clocks; secondly, a small subset of pulsars, millisecond X-ray pulsars, provide all the necessary ingredients for a passive galactic positioning system. This is known in astronautics as X-ray pulsar-based navigation (XNAV). XNAV is comparable to GPS, except that it operates on a galactic scale. I propose a SETI-XNAV research program to test the hypothesis that this pulsar positioning system might be an instance of galactic-scale engineering by extraterrestrial beings. The paper starts by exposing the basics of pulsar navigation, continues with a critique of the rejection of the extraterrestrial hypothesis when pulsars were first discovered. The core section of the paper proposes lines of inquiry for SETI-XNAV, related to the pulsar distribution and power in the galaxy; their population; their evolution; possible pulse synchronizations; pulsar usability when navigating near the speed of light; decoding galactic coordinates; directed panspermia; and information content in pulses. Even if pulsars are natural, they are likely to be used as standards by ETIs in the galaxy. I discuss possible objections and potential benefits for humanity, whether the research program succeeds or not.