A circuit board mounted integrated circuit chip such as a processor is cooled by apparatus including a heat sink, a shroud and a fan. The heat sink includes a base placed on the top surface of the chip and fins extending up from the base. The shroud includes top and two opposed side walls closely enclosing the heat sink. The shroud is attached directly to the circuit board rather than to the heat sink or chip and can be used with chips and heat sinks that do not have special provision for attachment of the shroud. The fan moves cooling air through the shroud and between and around the heat sink fins. The fan is mounted to an end of the shroud and does not require clearance above the heat sink and shroud.