Single cesium atoms are cooled and trapped inside a small optical cavity by way of a novel far-off-resonance dipole-force trap, with observed lifetimes of 2-3 s. Trapped atoms are observed continuously via transmission of a strongly coupled probe beam, with individual events lasting approximately 1 s. The loss of successive atoms from the trap N>/=3-->2-->1-->0 is thereby monitored in real time. Trapping, cooling, and interactions with strong coupling are enabled by the trap potential, for which the center-of-mass motion is only weakly dependent on the atom's internal state.