A radiation-emitting chip (2) with a radiation-transmissive window (5), which has a refractive index n.sub.F and has a main area (19), with a multilayer structure (9), which contains a radiation-active layer (10) and adjoins the main area (19) of the window (5), and with a radiation-transmissive medium surrounding the window (5) and having the refractive index n.sub.0, the window (5) having at least two boundary areas (6, 7), which form an angle .beta., for which the relationship 90.degree.-.alpha..sub.t<.beta.<2.alpha..sub.t where .alpha..sub.t=arc sin(n.sub.0/n.sub.F) is satisfied. A radiation-emitting component contains a chip (2) of this type.