Since the Transformer architecture was introduced in 2017, there has been many attempts to bring the self-attention paradigm in the field of computer vision. In this paper, we propose LHC: Local multi-Head Channel self-attention, a novel self-attention module that can be easily integrated into virtually every convolutional neural network, and that is specifically designed for computer vision, with a specific focus on facial expression recognition. LHC is based on two main ideas: first, we think that in computer vision, the best way to leverage the self-attention paradigm is the channel-wise application instead of the more well explored spatial attention. Secondly, a local approach has the potential to better overcome the limitations of convolution than global attention, at least in those scenarios where images have a constant general structure, as in facial expression recognition. LHC-Net achieves a new state-of-the-art in the FER2013 dataset, with a significantly lower complexity and impact on the “host” architecture in terms of computational cost when compared with the previous state-of-the-art.