An LED light source has a housing having a base. A core projects from the base; is substantially cylindrical and is surrounded by tubes. The core and the base are arrayed about a longitudinal axis. A circuit board in the base supports LEDs. Each of the LEDs is positioned with one of the tubes in a one-to-one relationship at one end of the core. A heat sink is positioned in a heat-transferring relationship with the circuit board and a first reflector is attached to another end of the core. To direct the light emitted by the LEDs from the source to the reflector, the interior of the tubes can be plated with a highly reflective material. In one embodiment, each of the tubes is fitted with a light guide, each light guide extending from a position immediately above one of the LEDs to a position adjacent the reflector.