Attitude control of fixed-wing unmanned aerial vehicles (UAVs)is a difficult control problem in part due to uncertain nonlinear dynamics, actuator constraints, and coupled longitudinal and lateral motions. Current state-of-the-art autopilots are based on linear control and are thus limited in their effectiveness and performance. Deep reinforcement learning (DRL) is a machine learning method to automatically discover optimal control laws through interaction with the controlled system, that can handle complex nonlinear dynamics. We show in this paper that DRL can successfully learn to perform attitude control of a fixed-wing UAV operating directly on the original nonlinear dynamics, requiring as little as three minutes of flight data. We initially train our model in a simulation environment and then deploy the learned controller on the UAV in flight tests, demonstrating comparable performance to the state-of-the-art ArduPlaneproportional-integral-derivative (PID) attitude controller with no further online learning required. To better understand the operation of the learned controller we present an analysis of its behaviour, including a comparison to the existing well-tuned PID controller.