In this paper, we propose the first secure federated $χ^2$-test protocol Fed-$χ^2$. To minimize both the privacy leakage and the communication cost, we recast $χ^2$-test to the second moment estimation problem and thus can take advantage of stable projection to encode the local information in a short vector. As such encodings can be aggregated with only summation, secure aggregation can be naturally applied to hide the individual updates. We formally prove the security guarantee of Fed-$χ^2$ that the joint distribution is hidden in a subspace with exponential possible distributions. Our evaluation results show that Fed-$χ^2$ achieves negligible accuracy drops with small client-side computation overhead. In several real-world case studies, the performance of Fed-$χ^2$ is comparable to the centralized $χ^2$-test.