Optical frequency combs have become a very powerful tool in metrology and beyond, thanks to their ability to link radio frequencies with optical frequencies via a process known as self-referencing. Typical self-referencing is accomplished in two steps: the generation of an octave-spanning supercontinuum spectrum and the frequency-doubling of one part of that spectrum. Traditionally, these two steps have been performed by two separate optical components. With the advent of photonic integrated circuits, the combination of these two steps has become possible in a single small and monolithic chip. One photonic integrated circuit platform very well suited for on-chip self-referencing is lithium niobate on insulator—a platform characterized by high second and third order nonlinearities. Here, we show that combining a lithium niobate on insulator waveguide with a silicon photodiode results in a very compact and direct low-noise path toward self-referencing of mode-locked lasers. Using digital servo electronics, the resulting frequency comb is fully stabilized. Its high degree of stability is verified with an independent out-of-loop measurement and is quantified to be 6.8 mHz. Furthermore, we show that the spectrum generated inside the lithium niobate waveguide remains stable over many hours.