Utilizing two Chandra High Resolution Camera ( HRC-I ) observations with an epoch separation of somewhat more than five years , we have measured the proper motion of the central compact object , RX J0822-4300 , in the supernova remnant Puppis-A for the first time . The position of RX J0822-4300 is found to be different by 0.574 \pm 0.184 arcsec , implying a proper motion of 107.49 \pm 34.46 mas/yr with a position angle of 241 ^ { \circ } \pm 24 ^ { \circ } . For a distance of 2.2 kpc , this proper motion is equivalent to a recoil velocity of 1121.79 \pm 359.60 km/s . Both the magnitude and the 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 . 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 .