A giant low-frequency, in-plane dielectric constant, ϵ ∼ 106, for epitaxial thin films of Ca1−xLaxMnO3 (x ⩽ 0.03) was observed over a broad temperature range, 4 K ⩽ T ⩽ 300 K. This phenomenon is attributed to an internal barrier-layer capacitor (IBLC) structure, with Schottky contacts between semiconducting grains. The room-temperature ϵ increases substantially with electron (La) doping, consistent with a simple model for IBLCs. The measured values of ϵ exceed those of conventional two-phase IBLC materials based on (Ba,Sr)TiO3 as well as on recently discovered CaCu3Ti4O12 and (Li,Ti)-doped NiO.