ABSTRACT We present constraints on the mean dark energy density, ΩX and dark energy equation of state parameter, wX, 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 r2500 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 Λ cold dark matter (CDM) cosmology with the curvature ΩK included as a free parameter, we find ΩΛ= 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 ΩX= 0.75 ± 0.04, Ωm= 0.26+0.06−0.04 and wX=−1.26 ± 0.24. Imposing the prior constraint wX > −1, the same data require wX < −0.7 at 95 per cent confidence. Similar results on the mean matter density and dark energy equation of state parameter, Ωm= 0.24 ± 0.04 and wX=−1.20+0.24−0.28, are obtained by replacing the cosmic microwave background data with standard priors on the Hubble constant and mean baryon density and assuming a flat geometry.