We present LCollision, a learning-based method that synthesizes collision-free 3D human poses. At the crux of our approach is a novel deep architecture that simultaneously decodes new human poses from the latent space and predicts colliding body parts. These two components of our architecture are used as the objective function and surrogate hard constraints in a constrained optimization for collision-free human pose generation. A novel aspect of our approach is the use of a bilevel autoencoder that decomposes whole-body collisions into groups of collisions between localized body parts. By solving the constrained optimizations, we show that a significant amount of collision artifacts can be resolved. Furthermore, in a large test set of 2.5 x $10^6$ randomized poses from SCAPE, our architecture achieves a collision-prediction accuracy of 94.1% with 80x speedup over exact collision detection algorithms. To the best of our knowledge, LCollision is the first approach that accelerates collision detection and resolves penetrations using a neural network.