We demonstrate a light emitting p-i-n diode made of a highly aligned film of separated (99%) semiconducting carbon nanotubes, self-assembled from solution. By using a split gate technique, we create p- and n-doped regions in the nanotube film that are separated by a micron-wide gap. We inject p- and n-type charge carriers into the device channel from opposite contacts and investigate the radiative recombination using optical micro-spectroscopy. We find that the threshold-less light generation efficiency in the intrinsic carbon nanotube film segment can be enhanced by increasing the potential drop across the junction, demonstrating the LED-principle in a carbon nanotube film for the first time. The device emits infrared light that is polarized along the long axes of the carbon nanotubes that form the aligned film.