  The coherence of a hyperfine-state superposition of a trapped $^{9}$Be$^+$
ion in the presence of off-resonant light is experimentally studied. It is
shown that Rayleigh elastic scattering of photons that does not change state
populations also does not affect coherence. Coherence times exceeding the
average scattering time of 19 photons are observed. This result implies that,
with sufficient control over its parameters, laser light can be used to
manipulate hyperfine-state superpositions with very little decoherence.
