We propose Chirality Nets, a family of deep nets that is equivariant to the "chirality transform", i.e., the transformation to create a chiral pair. Through parameter sharing, odd and even symmetry, we propose and prove variants of standard building blocks of deep nets that satisfy the equivariance property, including fully connected layers, convolutional layers, batch-normalization, and LSTM/GRU cells. The proposed layers lead to a more data efficient representation and a reduction in computation by exploiting symmetry. We evaluate chirality nets on the task of human pose regression, which naturally exploits the left/right mirroring of the human body. We study three pose regression tasks: 3D pose estimation from video, 2D pose forecasting, and skeleton based activity recognition. Our approach achieves/matches state-of-the-art results, with more significant gains on small datasets and limited-data settings.