Photonically integrated resonators are promising as a platform for enabling ultranarrow linewidth lasers in a compact form factor. Owing to their small size, these integrated resonators suffer from thermal noise that limits the frequency stability of the optical mode to ∼100 kHz. Here, we demonstrate an integrated stimulated Brillouin scattering (SBS) laser based on a large mode-volume annulus resonator that realizes an ultranarrow thermal-noise-limited linewidth of 270 Hz. In practice, yet narrower linewidths are required before integrated lasers can be truly useful for applications such as optical atomic clocks, quantum computing, gravitational wave detection, and precision spectroscopy. To this end, we employ a thermorefractive noise suppression technique utilizing an auxiliary laser to reduce our SBS laser linewidth to 70 Hz. This demonstration showcases the possibility of stabilizing the thermal motion of even the narrowest linewidth chip lasers to below 100 Hz, thereby opening the door to making integrated microresonators practical for the most demanding future scientific endeavors.