Measurements in the temperature range 0.4 to 3°K have shown that the specific heat of American Smelting and Refining Co. 99.999+% pure copper in the ``as received'' condition may be higher than the specific heat of samples which have been vacuum annealed or vacuum cast from this material, possibly due to the presence of a dissolved gas. The specific heat of copper has been increased (by a percent or so) by heating in a hydrogen atmosphere. The effect of very low levels of transition metal impurities on the specific heat is discussed.