  We present experimental evidence for a coherent superposition of
macroscopically distinct flux states in an rf-SQUID. When the external flux
Phi_x applied to the SQUID is near 1/2 of a flux quantum Phi_0, the SQUID has
two nearly degenerate configurations: the zero- and one-fluxoid states,
corresponding to a few microamperes of current flowing clockwise or
counterclockwise, respectively. The system is modeled as a particle in a
double-well potential where each well represents a distinct fluxoid state (0 or
1) and the barrier between the wells can be controlled in situ. For low damping
and a sufficiently high barrier, the system has a set of quantized energy
levels localized in each well. The relative energies of these levels can be
varied with Phi_x. External microwaves are used to pump the system from the
well-localized ground state of one well into one of a pair of excited states
nearer the top of the barrier. We spectroscopically map out the energy of these
levels in the neighborhood of their degeneracy point by varying Phi_x as well
as the barrier height. We find a splitting between the two states at this
point, when both states are below the classical energy barrier, indicating that
the system attains a coherent superposition of flux basis states that are
macroscopically distinct in that their mean fluxes differ by more than 1/4
Phi_0 and their currents differ by several microamperes.
