We present TetGAN, a convolutional neural network designed to generate tetrahedral meshes. We represent shapes using an irregular tetrahedral grid which encodes an occupancy and displacement field. Our formulation enables defining tetrahedral convolution, pooling, and upsampling operations to synthesize explicit mesh connectivity with variable topological genus. The proposed neural network layers learn deep features over each tetrahedron and learn to extract patterns within spatial regions across multiple scales. We illustrate the capabilities of our technique to encode tetrahedral meshes into a semantically meaningful latent-space which can be used for shape editing and synthesis.