Topological superconductors represent a newly predicted phase of matter that is topologically distinct from conventional superconducting condensates of Cooper pairs. As a manifestation of their topological character, topological superconductors support solid-state realizations of Majorana fermions at their boundaries. The recently discovered superconductor Cu(x)Bi(2)Se(3) has been theoretically proposed as an odd-parity superconductor in the time-reversal-invariant topological superconductor class, and point-contact spectroscopy measurements have reported the observation of zero-bias conductance peaks corresponding to Majorana states in this material. Here we report scanning tunneling microscopy measurements of the superconducting energy gap in Cu(x)Bi(2)Se(3) as a function of spatial position and applied magnetic field. The tunneling spectrum shows that the density of states at the Fermi level is fully gapped without any in-gap states. The spectrum is well described by the Bardeen-Cooper-Schrieffer theory with a momentum independent order parameter, which suggests that Cu(x)Bi(2)Se(3) is a classical s-wave superconductor contrary to previous expectations and measurements.