Continued improvements in the manufacturing of Cd1-xZnxTe (CZT) material have resulted in a practical thermoelectrically cooled X-ray and gamma-ray detector of very high energy resolution. A high resolution spectroscopy system was used to measure the Fano factor in CZT at temperatures down to -40 degrees C. The best resolution of the 5.9 keV Fe-55 peak was measured to be 188 eV FWHM, while the best resolution of the 59.5 keV Am-241 peak was measured to be 482 eV FWHM. The minimum measured Fano factor was 0.082, with several measurements yielding a value of 0.089+/-0.005. With a resolution of 4.2 keV FWHM for the 662 keV peak of Cs-137, these detectors demonstrate excellent performance in detecting X-rays and gamma rays.