We describe an ultraviolet (uv) diode laser system for cooling trapped Yb(+) ions. Using four stages of thermoelectric cooling, 10 mW of light at 369.5 nm is obtained by cooling a 373.4-nm uv diode to approximately -20 degrees C. Frequency stabilization is provided by a diffraction grating mounted in the Littrow configuration which allows for a mode-hop free tuning range of approximately 25 GHz. In order to avoid water condensation, the diode laser and associated optics are placed inside an evacuated chamber. Saturated absorption spectroscopy utilizing an Yb hollow cathode lamp is performed. This laser system is currently being used to cool single ions in an experiment whose ultimate goal is to look for modern variation of the fine-structure constant.