Is there a cosmological constant?

We present limits on the cosmological constant from the statistics of gravitational lenses using newly completed quasar surveys, new lens data, and a range of lens models. The formal limits are lambda(0) < 0.66 at 95% confidence in flat cosmologies (Omega(0) + lambda(0) = 1) and Omega(0) > 0.15 at 90% confidence in open universes (lambda(0) = 0), including the statistical uncertainties in the number of lenses, galaxies, and quasars and the parameters relating galaxy luminosities to dynamical variables. The limit holds for either softened isothermal or de Vaucouleurs models of the lens galaxies, suggesting that the radial mass distribution in the lens galaxy is not a significant systematic uncertainty. The cosmological limits are unaffected by adding a small core radius to the isothermal lens models or by the luminosity of the lens galaxy. Inconsistent models of the effects of a core radius make significant errors in the cosmological constraints. Extinction in E/S0 galaxies can significantly reduce the limits on the cosmological constant, but changing the expected number of lenses by a factor of 2 requires a minimum of 100 times more dust than is observed locally in E/S0 galaxies. Rapid evolution of the lenses is the most promising means of evading these limits. However, a viable model must not only reduce the expected number of lenses but do so without significantly altering the average image separations, magnitudes, and redshifts and the relative properties of optically and radio selected lenses.