The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance, and the analyst must make real-time decisions until a stopping criterion is reached. In this work, we study the sequential hypothesis testing problem under the constraint of Renyi differential privacy for the sample. Unlike previous work in private hypothesis testing that focuses on the classical fixed sample setting, our results may allow a conclusion to be reached much earlier, and thus saves the cost of collecting these additional samples. We present a new private algorithm based on Wald's Sequential Probability Ratio Test (SPRT) that gives strong theoretical privacy guarantees. We provide theoretical analysis on statistical performance measured by Type I and Type II error as well as the expected sample size, and we also provide empirical validation of our results.