Electrical transport measurements were made on single-crystal nanowires to understand the intrinsic dissipation mechanisms of a one-dimensional superconductor. While the resistance of wires of diameter larger than drops precipitously to zero at near , a residual resistive tail extending down to low temperature is found for wires with diameters of 20 and . As a function of temperature, the logarithm of the residual resistance appears as two linear sections, one within a few tenths of a degree below and the other extending down to at least , the minimum temperature of the measurements. The residual resistance is found to be ohmic at all temperatures below of . These findings are suggestive of a thermally activated phase slip process near and quantum fluctuation-induced phase slip process in the low-temperature regime. When the excitation current exceeds a critical value, the voltage-current characteristics show a series of discrete steps in approaching the normal state.