With the advent of machine learning applications to physical layer communications problems, neural networkbased auto-encoders are considered for channel state information (CSI) feedback of closed-loop MIMO operations. An autoencoder consists of an encoder and a decoder, where the “bottleneck” connecting the encoder and the decoder can be used for CSI feedback. The quantization process is usually applied to the –bottleneck” for the CSI feedback channel. This paper proposes a new approach without an explicit quantization step for CSI coding. The new proposal, known as binary variational (BiV) CSI coding, is based on the variational autoencoder (VAE) framework, with a Bernoulli distribution assumed for the latent space. A binary sampling step provides binary samples of the latent vector for the variational encoder. The encoder and decoder of the BiV CSI coding can be trained together with the stochastic gradient descent (SGD) method. Several trained BiV models are provided to demonstrate the effectiveness of the BiV CSI coding for 3GPP-based MIMO channels.