In an LED array comprising a plurality of radiation-emitting semiconductor chips each of which has a radiation outcoupling surface, the radiation emitted by the semiconductor chips being outcoupled substantially through said radiation outcoupling surface, and a cover body that is transparent to the emitted radiation, the transparent cover body comprises, on a surface facing toward the radiation outcoupling surfaces of the semiconductor chips, one or more conductive traces made of a conductive material that is transparent to the emitted radiation, and the semiconductor chips each comprise, on the radiation outcoupling surface, at least one electrical contact that is connected to the conductive trace or to at least one of the plurality of conductive traces. At least one luminescence conversion material is contained in the transparent cover body and/or applied in a layer to the cover body and/or the semiconductor chips.