A medical illumination unit (1) has an LED chip (15) and a rod-shaped body (5) with a proximal end (11) and a distal end (7). A distal hollow section (9) begins before the distal end (7) and reaches the distal end (7), and a supply lead section (12) begins at the proximal end (11) and reaches the distal hollow section (9). The LED chip (15) is in the distal hollow section of the rod-shaped body (5) and is supplied with energy through the supply lead (12). A luminescent converter is between the LED chip (15) and the distal end (7) of the rod-shaped or tubular body or at the distal end of the rod-shaped body (5), the converter properties of which are selected to convert light emitted by the LED chip (15) into light with a desired wavelength distribution.