Surface acoustic waves (SAWs) enable a wide array of technologies, including radiofrequency filters1,2, chemical and biological sensors3–5, acousto-optic devices6–8, acoustic control of microfluidic flow in lab-on-a-chip systems9–11 and quantum phononics12–19. Although numerous methods exist for generating SAWs, they each have intrinsic limitations that inhibit performance, operation at high frequencies and use in systems constrained in size, weight and power. Here we present a completely solid-state, single-chip SAW phonon laser consisting of a lithium niobate SAW resonator with an internal, d.c. electrically injected and broadband semiconductor gain medium with <0.15 mm2 footprint. Below the threshold bias of 36 V, the device behaves as a resonant amplifier, and above it exhibits self-sustained coherent oscillation, linewidth narrowing and high output powers. A continuous on-chip acoustic output power of up to −6.1 dBm is generated at 1 GHz with a resolution-limited linewidth of <77 Hz and a carrier phase noise of −57 dBc Hz−1 at 1 kHz offset. Through detailed modelling, we show pathways for improving the performance of these devices, including mHz linewidths, high power efficiencies and footprints under 550 μm2 at 10 GHz. This demonstration paves the way for ultrahigh-frequency SAW sources on-chip and highly miniaturized SAW-based systems that can be operated without an external radiofrequency source.