The investigation of the presence of structural change in economic and financial series is a major preoccupation in econometrics. A number of tests have been developed and used to explore the stationarity properties of various processes. Most of the focus has rested on the first two moments of a process thereby implying that these tests are tests of covariance stationarity. We propose a new test for strict stationarity, that considers the whole distribution of the process rather than just its first two moments, and examine its asymptotic properties. We provide two alternative bootstrap approximations for the exact distribution of the test statistic. A Monte Carlo study illustrates the properties of the new test and an empirical application to the constituents of the S&P 500 illustrates its usefulness.