A luminaire and an illumination system are disclosed. In an embodiment a luminaire includes at least one light-emitting semiconductor chip having a main emission side and a reflector having a reflection side facing the main emission side, the reflection side being a freeform different from a circle, an ellipse, a parabola or a hyperbola when seen in cross-section, wherein a base line of the reflector runs through the main emission side and a local height of the reflection side is measured against the base line, wherein a local focal length of the reflection side is increased along the local height, concerning ray bundles coming in parallel with the base line from an exterior of the luminaire during operation, and wherein local heights do not have a common focal point.