Gold nanorods capped with micelles and having an aspect ratio of 2.0-5.4 are found to fluoresce with a quantum yield which is over a million times that of the metal. For rods of the same width, the yield is found to increase quadratically while the wavelength maximum increases linearly with the length. We assign this emission to the electron and hole interband recombination. The increase in the emission yield results from the enhancement effect of the incoming and outgoing electric fields via coupling to the surface plasmon resonance in the rods. This is similar to the previously proposed fluorescence and the Raman enhancement on noble metal rough surfaces.