Architecture of the front-end electronics for the ATLAS muon precision chamber (MDT) is presented. Especially, test results of a prototype TDC chip are described in detail. The chip was fabricated in a 0.3 μm CMOS Gate-Array technology. Measurements of critical elements of the chip such as the PLL, and data buffering circuits demonstrated adequate performance. The effect of gamma-ray irradiation, using a 60Co source, and neutron irradiation, were also examined. The test results revealed radiation tolerance adequate for the operation of the circuits in the environment of the ATLAS MDT. Mounting of the front-end electronics to the MDT is scheduled to start in the year 2001.