The goal of the paper is to propose an optimal statistical test for the steganalysis of Jsteg algorithm. The test is based on a state-of-the-art statistical model of quantized Discrete Cosine Transform (DCT) coefficients that allows us to reliably detect any small change in a cover image due to hidden information. By formulating the hidden information detection as a hypothesis testing problem, the paper designs the most powerful Likelihood Ratio Test (LRT) assuming that all model parameters are perfectly known. The statistical performance of the LRT is analytically provided. Numerical results and comparison with other detectors highlight the relevance of the proposed approach.