We describe a hydrogen maser oscillator that has been designed to operate as a highly stable clock operating at temperatures below 1 K using a film of superfluid helium 4 as a storage volume wall coating. We derive the expressions that predict the statistically determined frequency stability of the maser in terms of the maser's internal parameters. Our design follows conventional atomic beam state selection techniques for supplying atoms in the F = 1, mF = 0 hyperfine sublevel to the oscillating region, which is located inside a sapphire dielectrically loaded TE011-mode cavity resonator. Measurements of the Hydrogen-Helium wallshift and the line Q of the maser oscillator have been made with unsaturated superfluid helium films at temperatures between 0.475 and 0.575 K. These show that the wallshift depends strongly on film thickness and that the Q of the maser oscillator improves very rapidly as film thickness is increased.