Downhole orientation sensing with a nuclear spin gyroscope. A downhole orientation sensing system for use in conjunction with a subterranean well can include a downhole instrument assembly positioned in the well, the instrument assembly including an atomic comagnetometer, and at least one optical waveguide which transmits light between the atomic comagnetometer and a remote location. A method of sensing orientation of an instrument assembly in a subterranean well can include incorporating an atomic comagnetometer into the instrument assembly, and installing the instrument assembly in the well.