We develop differentially private hypothesis testing methods for the small sample regime. Given a sample $\cal D$ from a categorical distribution $p$ over some domain $Σ$, an explicitly described distribution $q$ over $Σ$, some privacy parameter $\varepsilon$, accuracy parameter $α$, and requirements $β_{\rm I}$ and $β_{\rm II}$ for the type I and type II errors of our test, the goal is to distinguish between $p=q$ and $d_{\rm{TV}}(p,q) \geq α$. We provide theoretical bounds for the sample size $|{\cal D}|$ so that our method both satisfies $(\varepsilon,0)$-differential privacy, and guarantees $β_{\rm I}$ and $β_{\rm II}$ type I and type II errors. We show that differential privacy may come for free in some regimes of parameters, and we always beat the sample complexity resulting from running the $χ^2$-test with noisy counts, or standard approaches such as repetition for endowing non-private $χ^2$-style statistics with differential privacy guarantees. We experimentally compare the sample complexity of our method to that of recently proposed methods for private hypothesis testing.