In a pilot study of the dielectric constant of room-temperature ionic liquids, we use dielectric spectroscopy in the megahertz/gigahertz regime to determine the complex dielectric function of five 1-alkyl-3-methylimidazolium salts, from which the static dielectric constant epsilon is obtained by zero-frequency extrapolation. The results classify the salts as moderately polar solvents. The observed epsilon-values at 298.15 K fall between 15.2 and 8.8, and epsilon decreases with increasing chain length of the alkyl residue of the cation. The anion sequence is trifluoromethylsulfonate > tetrafluoroborate tetrafluorophosphate. The results indicate markedly lower polarities than found by spectroscopy with polarity-sensitive solvatochromic dyes.