An IC chip package, in one embodiment, may include an IC chip including an upper surface including an overhang extending beyond a sidewall of the IC chip, and underfill material about the sidewall and under the overhang. The overhang prevents underfill material from extending over an upper surface of the IC chip. In another embodiment, a ball grid array (BGA) is first mounted to landing pads on a lower of two joined IC chip packages. Since the BGA is formed on the lower IC chip package first, the BGA acts as a dam for the underfill material thereon. The underfill material extends about the respective IC chip and surrounds a bottom portion of a plurality of solder elements of the BGA and at least a portion of respective landing pads thereof.