Today’s precision experiments for timekeeping, inertial sensing, and fundamental science place strict requirements on the spectral distribution of laser frequency noise. Rubidium-based experiments utilize table-top 780 nm laser systems for high-performance clocks, gravity sensors, and quantum gates. Wafer-scale integration of these lasers is critical for enabling systems-on-chip. Despite progress towards chip-scale 780 nm ultra-narrow linewidth lasers, achieving sub-Hz fundamental linewidth and sub-kHz integral linewidth has remained elusive. Here we report a hybrid integrated 780 nm self-injection locked laser with 0.74 Hz fundamental and 864 Hz integral linewidths and thermorefractive-noise-limited 100 Hz2/Hz at 10 kHz. These linewidths are over an order of magnitude lower than previous photonic-integrated 780 nm implementations. The laser consists of a Fabry-Pérot diode edge-coupled to an on-chip splitter and a tunable 90 million Q resonator realized in the CMOS foundry-compatible silicon nitride platform. We achieve 2 mW output power, 36 dB side mode suppression ratio, and a 2.5 GHz mode-hop-free tuning range. To demonstrate the potential for quantum atomic applications, we analyze the laser noise influence on sensitivity limits for atomic clocks, quantum gates, and atom interferometer gravimeters. This technology can be translated to other atomic wavelengths, enabling compact, ultra-low noise lasers for quantum sensing, computing, and metrology.