Speckle interferometry is a powerful tool for close binary star research allowing angular resolutions as small as 20 milliarcsecond. A technique is proposed to resolve spectroscopic binaries with even smaller separations. It uses the fact that speckle images taken in one or the other of the Doppler shifted spectral lines give a different intensity weighting of the two components of the binary. The location of the speckles in the two speckle images is therefore different, the direction of the displacement being related to the position angle of the binary, the amount of the displacement being related to its separation. Since the location of speckles can be determined with a much higher precision than their diameter, this creates the possibility for submilliarcsecond observations. This paper describes an experiment being started now to use this so-called “Differential Speckle Interferometry” technique for the study of binaries, stellar rotation, stellar chromospheres, Ap stars and other objects.