Neural speech synthesis models have recently demonstrated the ability to synthesize high quality speech for text-to-speech and compression applications. These new models often require powerful GPUs to achieve real-time operation, so being able to reduce their complexity would open the way for many new applications. We propose LPCNet, a WaveRNN variant that combines linear prediction with recurrent neural networks to significantly improve the efficiency of speech synthesis. We demonstrate that LPCNet can achieve significantly higher quality than WaveRNN for the same network size and that high quality LPCNet speech synthesis is achievable with a complexity under 3 GFLOPS. This makes it easier to deploy neural synthesis applications on lower-power devices, such as embedded systems and mobile phones.