The Alfven and Mendis (1977) conclusion that dust grains in galaxies render the universe opaque to cosmic microwave background at a red shift ratio equal to 40 is challenged by a calculation of the opacity of galactic dust grains to the microwave background radiation from the time of decoupling at emission red shift ratio equal to 1500 to the present in the standard big bang model. In the present calculation, evolutionary effects on grain opacity and abundance are estimated. At wavelengths used in studying the microwave background, the optical depth of the grains is found to be 0.18 when the deceleration parameter equals 0.03, and 0.05 when the deceleration parameter equals 0.5. The results indicate that microwave background can provide information on an early dense phase of the universe.