The melting transition of DNA, whereby the strands of the double-helix structure completely separate at a certain temperature, has been characterized using neutron scattering. A Bragg peak from B-form fiber DNA has been measured as a function of temperature, and its widths and integrated intensities have been interpreted using the Peyrard-Bishop-Dauxois model with only one free parameter. The experiment is unique, as it gives spatial correlation along the molecule through the melting transition where other techniques cannot.