  We demonstrate a sensitive method of charge detection based on
radio-frequency readout of the Josephson inductance of a superconducting
single-electron transistor. Charge sensitivity $1.4 \times 10^{-4}e/\sqrt{Hz}$,
limited by preamplifier, is achieved in an operation mode which takes advantage
of the nonlinearity of the Josephson potential. Owing to reactive readout, our
setup has more than two orders of magnitude lower dissipation than the existing
method of radio-frequency electrometry. With an optimized sample, we expect
uncoupled energy sensitivity below $\hbar$ in the same experimental scheme.
