(Abriged) We present the analysis of the baryonic content of 52 X-ray luminous galaxy clusters observed with Chandra in the redshift range 0.3-1.273. We use the deprojected X-ray surface brightness profiles and the measured values of the gas temperature to recover the gas and total mass profiles. By assuming that galaxy clusters are representative of the cosmic baryon budget, the distribution of the cluster baryon fraction in the hottest (T> 4 keV) systems as a function of redshift is used to constrain the cosmological parameters. We discuss how our constraints are affected by several systematics, namely the isothermality, the assumed baryon fraction in stars, the depletion parameter and the sample selection. By using only the cluster baryon fraction as a proxy for the cosmological parameters, we obtain that Omega is very well constrained at the value of 0.35 with a relative statistical uncertainty of 11% (1 sigma level; w=-1) and a further systematic error of about (-6,+7)%. On the other hand, constraints on Lambda (without the prior of flat geometry) and w (using the prior of flat geometry) are definitely weaker due to the presence of larger statistical and systematic uncertainties (of the order of 40 per cent on Lambda and larger than 50 per cent on w). If the WMAP 5-year best-fit results are assumed to fix the cosmological parameters, we limit the contributions expected from non-thermal pressure support and ICM clumpiness to be lower than about 10 per cent, leaving also room to accommodate baryons not accounted for either in the X-ray emitting plasma or in stars of the order of 18 per cent of the total cluster baryon budget. ; Comment: A&A in press. Accepted on March 28, 2009. Revised to match version in print