Chandra X-ray observations of rich, dynamically relaxed galaxy clusters allow the properties of the X-ray gas and the total gravitating mass to be determined precisely. By combining Chandra results on the X-ray gas mass fractions in clusters with independent measurements of the Hubble constant and the mean baryonic matter density of the universe, we obtain a tight constraint on the mean matter density of the universe, Ωm, and an interesting constraint on the dark energy density, ΩΛ. Using these results, together with the observed local X-ray luminosity function of the most X-ray luminous galaxy clusters, a mass-luminosity relation determined from Chandra and ROSAT X-ray data and weak gravitational lensing observations, and the mass function predicted by numerical simulations, we also obtain a precise constraint on the normalization of mass fluctuations in the nearby universe, σ8.