Distributed feedback laser diodes (DFBs) serve as simple, compact, narrow-band light sources supporting a wide range of photonic applications. Typical linewidths are on the order of sub-MHz for free-running III-V DFBs at infrared wavelengths, but linewidths of short-wavelength GaN-based DFBs are considerably worse or unreported. Here, we present a free-running InGaN DFB operating at 443 nm with an intrinsic linewidth of 685 kHz at a continuous wave output power of 40 mW. This performance is achieved using a first-order embedded hydrogen silsesquioxane (HSQ) surface grating. The frequency noise is measured using a cross-correlated self-heterodyne frequency discriminator, and two estimations of integrated linewidth are evaluated using 1/π integration and β-separation line integration methods.