We propose an audio effects processing framework that learns to emulate a target electric guitar tone from a recording. We train a deep neural network using an adversarial approach, with the goal of transforming the timbre of a guitar, into the timbre of another guitar after audio effects processing has been applied, for example, by a guitar amplifier. The model training requires no paired data, and the resulting model emulates the target timbre well whilst being capable of real-time processing on a modern personal computer. To verify our approach we present two experiments, one which carries out unpaired training using paired data, allowing us to monitor training via objective metrics, and another that uses fully unpaired data, corresponding to a realistic scenario where a user wants to emulate a guitar timbre only using audio data from a recording. Our listening test results confirm that the models are perceptually convincing.