While the defining features of spiral galaxies are the beautiful arms that they display, the exact nature of such spiral structures is still an open question. Since the 1960s, it has been widely assumed that spiral arms in galaxies with two distinct symmetrical arms (known as "grand design" systems) are the products of density waves that propagate around the disk as a persistent pattern, with the spiral arms being visibly enhanced by the star formation that is triggered as the passing wave compresses gas in the galaxy disk. Such a persistent wave would propagate with an approximately constant angular speed called its pattern speed, ΩP, and so a simple test of the density-wave theory is to measure this quantity and show that it does not vary with radius in the galaxy. Unfortunately, this measurement is difficult because ΩP only has an indirect connection to readily-measurable quantities such as the stellar rotation speed. Here, we make use of the detailed information on stellar populations that can now be extracted from spectral mapping of a grand-design spiral galaxy (UGC 3825) to measure the offset between young stars of a known age and the spiral arm in which they formed, allowing the first direct measure of ΩP at a range of radii. The offset in this galaxy is found to be as expected for a pattern speed that varies little with radius, vindicating the global spiral density wave theory and establishing the reliability of this new method.