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Efficient imaging of biomolecules, two-dimensional materials, and electromagnetic fields depends on retrieval of the phase of transmitted electrons. We demonstrate a method to measure phase in a scanning transmission electron microscope (STEM) using a nanofabricated diffraction grating to produce multiple probe beams. The measured phase is more interpretable than phase-contrast scanning transmission electron microscopy techniques without an off-axis reference wave, and the resolution could surpass that of off-axis electron holography. We apply this technique, called STEM holography, to image nanoparticles, carbon substrates, and electric fields. The contrast observed in experiments agrees well with contrast predicted in simulations.