M stars constitute 75% of main sequence stars though, until recently, their star systems have not been considered suitable places for habitable planets to exist. In this study the climate of a synchronously rotating planet around an M dwarf star is evaluated using a three-dimensional global atmospheric circulation model. The presence of clouds and evaporative cooling at the surface of the planet result in a cooler surface temperature at the subsolar point. Water ice forms at the polar regions and on the dark side, where the minimum temperature lies between -30 degrees C and 0 degrees C. As expected, rainfall is extremely high on the starlit side and extremely low on the dark side. The presence of a dry continent causes higher temperatures on the dayside, and allows accumulation of snow on the nightside. The absence of any oceans leads to higher day-night temperature differences, consistent with previous work. The present study reinforces recent conclusions that synchronously rotating planets within the circumstellar habitable zones of M dwarf stars should be habitable, and therefore M dwarf systems should not be excluded in future searches for exoplanets.