An EGR cooler comprises a cooling core having a plurality of passages for accommodating the flow of exhaust gas therethrough, an exhaust gas inlet chamber connected to the cooling core, for receiving exhaust gas from an internal combustion engine and passing the exhaust gas to the cooling core, and an exhaust gas outlet chamber separate from the exhaust gas inlet chamber and connected to the cooling core for receiving exhaust gas from the core. The cooler further includes means for permitting the controlled passage of exhaust gas from the exhaust gas inlet chamber to the exhaust gas outlet chamber without passing through the cooling core, said means being positioned upstream from the exhaust gas outlet chamber. Configured in this manner, the EGR cooler permits the mixing of cooled exhaust gas with uncooled exhaust to provide a desired exiting gas temperature that is below an exhaust gas dew point.