We report on the design, construction, and commissioning of a prototype aperture masking technology implemented at the Keck OSIRIS Imager: the holographic aperture mask. Holographic aperture masking (HAM) aims at (i) increasing the throughput of sparse aperture masking (SAM) by selectively combining all subapertures across a telescope pupil in multiple interferograms using a phase mask, and (ii) adding low-resolution spectroscopic capabilities. Using liquid-crystal geometric phase patterns, we manufacture a HAM mask that uses an 11-hole SAM design as the central component and a holographic component comprising 19 different subapertures. Thanks to a multilayer liquid-crystal implementation, the mask has a diffraction efficiency higher than 96% from 1.1 to 2.5 micron. We create a pipeline that extracts monochromatic closure phases from the central component as well as multiwavelength closure phases from the holographic component. We test the performance of the HAM mask in the laboratory and on-sky. The holographic component yields 26 closure phases with spectral resolutions between R$∼$6.5 and R$∼$15. On April 19, 2019, we observed the binary star HDS 1507 in the Hbb filter ($łambda_0 = 1638$ nm and $Δ łambda = 330$ nm) and retrieved a constant separation of 120.9 $± 0.5$ mas for the independent wavelength bins, which is in excellent agreement with literature values. For both the laboratory measurements and the observations of unresolved reference stars, we recorded nonzero closure phases – a potential source of systematic error that we traced to polarization leakage of the HAM optic. We propose a future upgrade that improves the performance, reducing this effect to an acceptable level. Holographic aperture masking is a simple upgrade of SAM with increased throughput and a new capability of simultaneous low-resolution spectroscopy that provides new differential observables.