We report on the observation of non-classical rotational inertia behavior in solid He-4 confined to an annular channel in a sample cell under torsional motion, demonstrating superfluid behavior. The effect shows up as an abrupt drop in the resonant oscillation period as the sample cell is cooled below 230 mK. Measurement of 17 solid samples allows us to map out the boundary of this superfluid-like solid or supersolid phase from the melting line up to 66 bars. This experiment indicates that superfluid behavior is found in all three phases of matter, gas, liquid and solid. This work is done in collaboration with Eunseong Kim and is supported by the Condensed Matter Physics program of NSF.