We present constraints on the mean dark energy density , \Omega _ { X } and dark energy equation of state parameter , w _ { X } , based on Chandra measurements of the X-ray gas mass fraction in 26 X-ray luminous , dynamically relaxed galaxy clusters spanning the redshift range 0.07 < z < 0.9 . Under the assumption that the X-ray gas mass fraction measured within r _ { 2500 } is constant with redshift and using only weak priors on the Hubble constant and mean baryon density of the Universe , we obtain a clear detection of the effects of dark energy on the distances to the clusters , confirming ( at comparable significance ) previous results from Type Ia supernovae studies . For a standard \Lambda CDM cosmology with the curvature \Omega _ { K } included as a free parameter , we find \Omega _ { \Lambda } = 0.94 ^ { +0.21 } _ { -0.23 } ( 68 per cent confidence limits ) . We also examine extended XCDM dark energy models . Combining the Chandra data with independent constraints from cosmic microwave background experiments , we find \Omega _ { X } = 0.75 \pm 0.04 , \Omega _ { m } = 0.26 ^ { +0.06 } _ { -0.04 } and w _ { X } = -1.26 \pm 0.24 . Imposing the prior constraint w _ { X } > -1 , the same data require w _ { X } < -0.7 at 95 per cent confidence . Similar results on the mean matter density and dark energy equation of state parameter , \Omega _ { m } = 0.24 \pm 0.04 and w _ { X } = -1.20 ^ { +0.24 } _ { -0.28 } , are obtained by replacing the CMB data with standard priors on the Hubble constant and mean baryon density and assuming a flat geometry .