Efficiency and resolution measurements are reported of an x-ray transmission grating to be flown on board the European X-ray Observatory Satellite (EXOSAT). By optimizing the thickness of the grating bars, very high efficiencies can be obtained over a limited energy range. An absolute efficiency of 20% at 7.1 A decreasing to 10% above 15 A has been achieved, including all effects of support structure and mounting necessary to withstand space qualification. This means that 10% of the incoming radiation at 7.1 A results in the minus first spectral order and 10% in the plus first order. The measured resolution at the short wavelength end of the range (lambda > 20 A) is determined by the mirror resolution; at the longer wavelengths (300 A), the effects of coma and astigmatism dominate. The measured resolution at 304 A for the EXOSAT-mirror-grating system is 4.5 A in agreement with theoretical predictions.