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 \pm 0.184 arcsec , implying a proper motion of \mu = 107.49 \pm 34.46 mas/yr . For a distance of 2.2 kpc , this proper motion is equivalent to a recoil velocity of 1121.79 \pm 359.60 km/s . The position angle is found to be 241 ^ { \circ } \pm 24 ^ { \circ } . 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 \sim 3 \sigma level only , one or more future HRC-I observations can obtain a much larger positional separation and further constrain the measurement .