A new technique to perform speckle interferometric measurements at J, H, K, L and M wavelengths is described. The time-averaged spatial frequency power spectrum of an image is obtained by scanning it successively over a series of gratings of differing spacing. Some measurements on a 1.5-m telescope are reported which show that diffraction-limited information is available at the near-infrared wavelengths. The point spread transfer functions of the speckle technique are predictably similar to ones measured at visible wavelengths. The size of the seeing disk at infrared wavelengths is measured and found to obey a lambda to the -1/5th power. Limiting speckle magnitudes for diffraction-limited resolution are generally derived and found to be approximately independent of telescope diameter. With long integration at a wavelength of 2.2 microns it should be possible to measure diffraction-limited information from sources with +12 mag.