A method of fabricating a chip package is provided. The chip package includes a laminate, a chip and conductive elements interposed between the chip and the laminate by which signals are transmitted among the chip and the laminate. The method includes dispensing a first underfill in a space defined between opposing faces of the chip and the laminate and dispensing a second underfill at least at a portion of an edge of the chip, the second underfill including a high aspect ratio material.