A novel technique is proposed for measuring the distributed strain and temperature in a fiber with a very high resolution. This technique makes use of the jagged appearance of Rayleigh backscatter traces from a single-mode fiber measured by using a coherent OTDR with a precisely frequency-controlled light source. Our preliminary experiment indicated the possibility of measuring temperature with a resolution of better than 0.01 and a spatial resolution of one meter. This temperature resolution is two orders of magnitude better than that provided by Brillouin-based distributed sensors.