The evolution of deep learning techniques has been transformative as they have allowed complex mappings to be trained between control inputs and outputs without the need for feature engineering. In this work, a myoelectric control system based on convolutional neural networks (CNN) is proposed as a possible alternative to traditional approaches that rely on specifically designed features. This CNN-based system is validated using a real-time Fitts' law style target acquisition test requiring single and combined wrist motions. The performance of the proposed system is then compared to that of a standard support vector machine (SVM) based myoelectric system using a set of time-domain features. Despite the prevalence and demonstrated performance of these well-known features, no significant difference (p>0.05) was found between the two methods for any of the computed control metrics. This demonstrates the potential for automated learning approaches to extract complex and rich information from stochastic biological signals. This first evaluation of the usability of a CNN in a real-time myoelectric control environment provides a basis for further exploration.