By making use of the sub-arcsecond angular resolution of the High Resolution Camera (HRC-I) aboard the Chandra X-ray satellite we have examined the central compact object RX J0822-4300 in the supernova remnant Puppis-A for a possible proper motion. Using data which span an epoch of 1952 days we found the position of RX J0822-4300 different by 0.574 +/- 0.184 arcsec, implying a proper motion of mu = 107.49 +/- 34.46 mas/yr. For a distance of 2.2 kpc, this proper motion is equivalent to a recoil velocity of 1121.79 +/- 359.60 km s(-1). The position angle is found to be 241. +/- 24.. Since both the magnitude and direction of the proper motion are in agreement with the birth place of RX J0822-4300 being near to the optical expansion center of the supernova remnant, the result presented in this letter is a promising indication of a fast moving compact object in a supernova remnant. Although the positional shift inferred from the current data is significant at a similar to 3 sigma level only, one or more future HRC-I observations can obtain a much larger positional separation and further constrain the measurement.