Complex reasoning over text requires understanding and chaining together free-form predicates and logical connectives. Prior work has largely tried to do this either symbolically or with black-box transformers. We present a middle ground between these two extremes: a compositional model reminiscent of neural module networks that can perform chained logical reasoning. This model first finds relevant sentences in the context and then chains them together using neural modules. Our model gives significant performance improvements (up to 29\% relative error reduction when comfibined with a reranker) on ROPES, a recently introduced complex reasoning dataset.