The 1H(e,e′K+)Λ reaction was studied as a function of the squared four-momentum transfer, Q2, and the virtual photon polarization, ɛ. For each of four Q2 settings, 0.52, 0.75, 1.00, and 2.00 (GeV/c)2, the longitudinal and transverse virtual photon cross sections were extracted in measurements at three virtual photon polarizations. The Q2 dependence of the σL/σT ratio differs significantly from current theoretical predictions. This, combined with the precision of the measurement, implies a need for revision of existing calculations.