A method of assembling a semiconductor chip to a substrate wherein at least one of the semiconductor chip and substrate comprise solder bumps. The method includes aligning the semiconductor chip with the substrate; applying a compression force to the semiconductor chip to cause the solder bumps to deform between the semiconductor chip pads and the substrate pads, the compression force being applied while the semiconductor chip and substrate are held at a temperature above room temperature and below a temperature at which any liquid will form in at least one of the solder bumps; then applying an underfill material to fill the gap between the chip and substrate; and then heating the assembled semiconductor chip and substrate to an elevated temperature to cause the solder bumps to melt and reflow and form a metallurgical bond between the semiconductor chip pads and the substrate pads.