We investigate the surface roughness of polycrystalline silicon core optical fibers fabricated using a high-pressure chemical deposition technique. By measuring the optical transmission of two fibers with different core sizes, we will show that scattering from the core-cladding interface has a negligible effect on the losses. A Zemetrics ZeScope three-dimensional optical profiler has been used to directly measure the surface of the core material, confirming a roughness of only ~0.1 nm. The ability to fabricate low-loss polysilicon optical fibers with ultrasmooth cores scalable to submicrometer dimensions should establish their use in a range of nonlinear optical applications.