Measuring stress changes within seismically active fault zones has been a long-sought goal of seismology. One approach is to exploit the stress dependence of seismic wave velocity, and we have investigated this in an active source cross-well experiment at the San Andreas Fault Observatory at Depth (SAFOD) drill site. Here we show that stress changes are indeed measurable using this technique. Over a two-month period, we observed an excellent anti-correlation between changes in the time required for a shear wave to travel through the rock along a fixed pathway (a few microseconds) and variations in barometric pressure. We also observed two large excursions in the travel-time data that are coincident with two earthquakes that are among those predicted to produce the largest coseismic stress changes at SAFOD. The two excursions started approximately 10 and 2 hours before the events, respectively, suggesting that they may be related to pre-rupture stress induced changes in crack properties, as observed in early laboratory studies.