The authors present data on the operation of thin-film superconducting strips of titanium as phonon sensors on the surface of silicon crystals. The superconducting films are biased at the foot of the resistive transition in temperature and below the critical latching current (the current above which a normal region in the film grows from self-heating). The interaction of an incident X-ray in the Si crystal generates a phonon source which propagates to the surface at the speed of sound. Such an event produces a several-microsecond-long self-terminating voltage pulse which is proportional to the amount of the sensor area driven normal. It is shown that these Ti superconducting transition edge sensors operated at 0.3 K have sufficient resolution for detecting particles with energy deposition above several keV, which makes them good candidates for use in neutrino (and other) experiments.