We use electron tunneling to measure electronic energy levels in individual nm-scale Al particles. For sufficiently large particles (greater than or equal to 5 nm in radius), the eigenstate energies reveal the existence of a superconducting excitation gap Omega which is driven continuously to zero by an applied magnetic field. The presence of Omega increases the voltage threshold for tunneling in a particle with an even number of electrons in its ground state, but decreases the tunneling threshold for an odd-electron particle. We discuss the roles of spin and orbital pair breaking in the magnetic-field transition.