We report the acquisition and deconvolution of three-dimensional spectrally resolved images in a programmable array microscope implementing a Hadamard transform fluorescence spectroscopy system with adjustable spectral resolution. A stack of 16 two-dimensional spectral images was collected at 400 nm intervals along the optical axis. The specimen consisted of a polytene chromosome spread from Drosophila melanogaster doubly labelled for the Polyhomeotic protein by indirect immunofluorescence labelling with Alexa594 and for DNA with YOYO-1. The resulting four-dimensional data set consisted of the xyz spatial dimensions (898 × 255 × 16) with a 26-point spectrum at each spatial location. The total exposure time to the sample was 34 min. The system requires the acquisition of multiple images, and thus works best with fluorophores that are resistant to photobleaching. Image deconvolution reduced the amount of out-of-focus blur by up to a factor of 8, resulting in a dramatic improvement in the visualization of the chromosome backbone and localization of the specific Polyhomeotic domains.