The electrical resistance of thin, 4-100 nm sputter-deposited (physical vapor deposition) Cu films was measured in situ in the deposition chamber. The Cu was deposited on silicon dioxide surfaces to reduce surface pinning or adhesion effects and allow high mobility. During, and following the deposition, the electrical resistance was measured under vacuum for periods of up to several thousand minutes, and in each case the electrical resistivity decreased 13%-50% over that time period. This is consistent with reports of room temperature grain growth in electrodeposited thin films. X-ray diffraction data showed significant increases in (111) crystallinity. At very small thicknesses (4.5 nm), it appears that a second mechanism occurs prior to grain growth which may be related to the agglomeration of nearly discontinuous islands on the surface. Similar Cu films deposited on Ta adhesion layers showed little, if any, change in resistance over time, indicating the role of the substrate interface in limiting grain growth.