We report precision heat capacity results of submonolayer and near monolayer 4He films adsorbed in porous silica-gel glass. Measurements were performed down to 0.1 K on films up to 26 μmole/m2. These coverages are below the critical value for superfluid onset and thought to be localized and solid-like. A coverage dependent heat capacity anomaly near 0.25 K was found, indicating a possible phase transition. © 1987 The Japan Society of Applied Physics.