An LED module has an electrically insulating main body, a base surface and a mounting surface located opposite the base surface. A number of electrical connection contacts are arranged at the mounting surface. The connection contacts do not adjoin the base surface. A heat sink is arranged in the main body. The heat sink extends from the mounting surface as far as the base surface. Furthermore, the LED module has a number of LED chips, each having an electrically insulating carrier substrate at a chip underside and two chip contacts at a chip top side. The LED chips are arranged with the electrically insulating carrier substrate on the heat sink.