The Transiting Exoplanet Survey Satellite (TESS) recently observed 18 transits of the hot Jupiter WASP-4b. The sequence of transits occurred 81.6 11.7 s earlier than had been predicted, based on data stretching back to 2007. This is unlikely to be the result of a clock error, because TESS observations of other hot Jupiters (WASP-6b, 18b, and 46b) are compatible with a constant period, ruling out an 81.6 s offset at the 6.4 level. The 1.3 day orbital period of WASP-4b appears to be decreasing at a rate of ms per year. The apparent period change might be caused by tidal orbital decay or apsidal precession, although both interpretations have shortcomings. The gravitational influence of a third body is another possibility, though at present there is minimal evidence for such a body. Further observations are needed to confirm and understand the timing variation.