We have studied the luminescence of narrow quantum wires at photoexcitation densities of up to similar to 3 x 10(6) cm(-1). We show that even at these densities, which are well above the expected Mott density of 8 x 10(5) cm(-1), excitonic recombination dominates over other recombination channels in stark contrast with the behavior of quantum wells and bulk structures at equivalent densities. As we observe no significant shift in the peak energy with density, an upper limit to the band gap renormalization can be set.