This paper presents a novel deep learning-based travel behaviour choice model. Our proposed Residual Logit (ResLogit) model formulation seamlessly integrates a Deep Neural Network (DNN) architecture into a multinomial logit model. Recently, DNN models such as the Multi-layer Perceptron (MLP) and the Recurrent Neural Network (RNN) have shown remarkable success in modelling complex and noisy behavioural data. However, econometric studies have argued that machine learning techniques are a ?black-box? and difficult to interpret for use in the choice analysis. We develop a data-driven choice model that extends the systematic utility function to incorporate non-linear cross-effects using a series of residual layers and using skipped connections to handle model identifiability in estimating a large number of parameters. The model structure accounts for cross-effects and choice heterogeneity arising from substitution, interactions with non-chosen alternatives and other effects in a non-linear manner. We describe the formulation, model estimation, interpretability and examine the relative performance and econometric implications of our proposed model. We present an illustrative example of the model on a classic red/blue bus choice scenario example. For a real-world application, we use a travel mode choice dataset to analyze the model characteristics compared to traditional neural networks and Logit formulations. Our findings show that our ResLogit approach significantly outperforms MLP models while providing similar interpretability as a Multinomial Logit model.