We propose a novel framework for 3D reassembly, the task of assembling a solid object from its broken pieces. The primary challenge in this under-explored problem is to robustly establish compatibility between parts from one object. Feature-based techniques have shown success in domains such as 3D similarity search; unfortunately, the global features typically employed to quantify whole-object similarity are unsuitable for identifying part-level compatibility. Therefore, we propose the use of local features which, in conjunction with robust matching, have become popular for object recognition in 2D images. This paper demonstrates that an analogous framework can be successful for 3D reassembly. Automating part-level compatibility enables the construction of an interactive system for 3D reassembly, where the user can easily assemble a desired object from a large collection of pieces (many of which are irrelevant) by iteratively selecting compatible parts. We evaluate our approach on a simulated database of broken objects and show that it scales well in the presence of noise and extraneous pieces.