A cryogenic hydrogen maser has been designed and constructed which will operate at temperatures near 10 K with a surface of frozen neon in the atom storage region. The atom storage region and microwave cavity are made from three pieces of single crystal sapphire. The neon surface is expected to be isothermal and stable to within 1 mK during operation. The sapphire is contained within a copper enclosure which is surrounded by magnetic shields and cooled by conduction to a helium-cooled copper plate. The helium cooling to the plate is in the form of cold helium gas flowing through a tube attached to the plate. A transition region made of G-11 fiberglass connects the sapphire cavity to the area containing the state-selection magnet. The internal vacuum of the maser is maintained by a helium-cooled cryopump located between the hydrogen atom source and the transition. Atomic hydrogen is supplied by an effusive discharge operated at liquid nitrogen temperatures. Much of the expected thermal characteristics have been experimentally verified. At temperatures near 10 K a stability of 1 mK was achieved for periods exceeding ninety minutes. Operation of the maser as a self-sustained oscillator awaits final tuning of the microwave cavity and development of the techniques required to prepare the neon surface.