We introduce Equivariant Neural Field Expectation Maximization (EFEM), a simple, effective, and robust geometric algorithm that can segment objects in 3D scenes without annotations or training on scenes. We achieve such unsupervised segmentation by exploiting single object shape priors. We make two novel steps in that direction. First, we introduce equivariant shape representations to this problem to eliminate the complexity induced by the variation in object configuration. Second, we propose a novel EM algorithm that can iteratively refine segmentation masks using the equivariant shape prior. We collect a novel real dataset Chairs and Mugs that contains various object configurations and novel scenes in order to verify the effectiveness and robustness of our method. Experimental results demonstrate that our method achieves consistent and robust performance across different scenes where the (weakly) supervised methods may fail. Code and data available at https://www.cis.upenn.edu/~leijh/projects/efem