The $^{12}$C(n, 2n)$^{11}$C cross section was measured from just below threshold to 26.5 MeV using the Pelletron accelerator at Ohio University. Monoenergetic neutrons, produced via the $^3$H(d,n)$^4$He reaction, were allowed to strike targets of polyethylene and graphite. Activation of both targets was measured by counting positron annihilations resulting from the $beta^+$ decay of $^{11}$C. Annihilation gamma rays were detected, both in coincidence and singly, using back-to-back NaI detectors. The incident neutron flux was determined indirectly via $^{1}$H(n,p) protons elastically scattered from the polyethylene target. Previous measurements fall into upper and lower bands, the results of the present measurement are consistent with the upper band.