We consider a test of an unknown change-point in a Weibull hazard function. We assume that data are subject to staggered entry and type I censoring. We formulate the profile log-likelihood ratio test statistic as a function of the changepoint and derive the limiting Gaussian process. From the supremum of the limiting process, we determine critical values and study the power of the test through simulation. We demonstrate this method using real data from a clinical study for the treatment of chronic granulomatous disease.