A HEISENBERG uncertainty relation exists between any two noncommuting variables of a quantum-mechanical system. In a superconductor, two such variables are the number, n, of Cooper pairs and the phase, phi, of the superconducting wavefunction. Suppressing fluctuations in either variable should lead to enhanced fluctuations in the other(1,2). To demonstrate this effect, we have fabricated a structure in which the quantum-mechanical fluctuations in the phase bf a superconducting grain can be suppressed. We measure the supercurrent that Rows through two Josephson tunnel junctions of small capacitance that are connected to the grain. The capacitance of the grain is itself so small that the number of Cooper pairs is well defined-charge transport through the grain is possible only through quantum-mechanical fluctuations in n. The phase of the grain is coupled to a large superconducting reservoir such that the fluctuations in phi can be controllably suppressed. The enhanced fluctuations in n that result from this coupling give rise to a large increase in the supercurrent through the grain.