We report on a windowless, high-density, gas-flow target at Jefferson Lab that was used to measure rp, the root-mean-square charge radius of the proton. The target achieved its design goal of an areal density of 2 × 1018 atoms/cm2, with the gas uniformly distributed over the 4 cm length of the cell and less than 1% residual gas outside the cell. This design eliminated scattering from the end caps of the target cell, a problem endemic to previous measurements of the proton charge radius in electron scattering experiments, and permitted a precise, model-independent extraction of rp by reaching unprecedentedly low values of Q2, the square of the electron's transfer of four-momentum to the proton.