Living with Large Lambda Philip Mannheim, Department of Physics, University of Connecticut With attempts to quench the cosmological constant $\Lambda$ having so far failed, we instead investigate what could be done if $\Lambda$ is not quenched and actually gets to be as big as elementary particle physics suggests. Since the quantity relevant to cosmology is actually $\Omega_{\Lambda}$, quenching it to its small measured value is equally achievable by quenching not $\Lambda$ but $G$ instead, with the $G$ relevant to cosmology then being much smaller than that measured in a low energy Cavendish experiment. To solve the cosmological constant problem we thus do not need to change or quench the energy content of the universe, but rather only its effect on cosmic evolution. A gravitational model in which this explicitly occurs, viz. conformal gravity, is presented, with the model being found to provide for a completely natural, non fine tuned accounting of the recent high $z$ accelerating universe supernovae data, no matter how big $\Lambda$ itself might actually be. Additionally, we show that unlike the standard gravity model where cosmic acceleration is only a recent phenomenon, the conformal gravity model remains accelerating at higher redshift. Detailed exploration of the Hubble plot beyond $z=1$ could thus be definitive for both models.