Knowledge of the abundance of H-3+ is needed in interstellar and planetary atmospheric chemistry. An important destruction mechanism of H-3+ is low-energy electron impact followed by dissociation, but estimates of the reaction rate span several orders of magnitude. As an attempt to resolve this uncertainty, the cross section for dissociative recombination of vibrationally cold H-3+ has been measured with an ion storage ring down to collision energies below 1 millielectron volt. A rate coefficient of 1.15 x 10(-7) cubic centimeters per second at 300 kelvin was deduced. The cross section scaled with collision energy according to E-1.15, giving the rate a temperature dependence of T-0.65.