Single-photon time-of-flight light detection and ranging (LiDAR) is a versatile technique for the measurement of absolute distances and for depth profiling. It has a wide variety of applications (e.g., land surveying, autonomous car navigation, underwater imaging) with the potential to achieve high-resolution three-dimensional images over long ranges when the key components of the measurement system are of a suitably high specification. In this work, a novel, high-efficiency, and low timing jitter superconducting nanowire single-photon detector, in conjunction with a custom single-pixel scanning transceiver system, and the time-correlated single-photon counting technique, enable the acquisition of millimeter-scale resolution depth images of scenes at standoff distances of hundreds of meters. A 1550 nm wavelength fiber laser was coupled to the monostatic transceiver to provide the illumination. The system was eye-safe with the maximum average optical output power being <= 3.5 mW for measurements of a scene at a standoff distance of 1 km. The overall system instrumental response was approximately 13 ps full width half maximum. This enabled 1 mm depth features on a reference board and a human head to be clearly resolved when measured by the system in broad daylight at standoff distances of 45 and 325 musing per-pixel acquisition times of between 0.25 and 1 ms. These high-resolution results demonstrate the enormous potential of such a system to acquire detailed depth and intensity images of scenes from long distances in daylight or darkness conditions. This could lead to step change improvements in applications such as facial and human activity recognition and the imaging of scenes through clutter and atmospheric obscurants. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.