We introduce a compressive sensing based approach for single pixel hyperspectral chemical imaging in a broad spectral range in the near-infrared. Fully integrated MEMS based Fabry-Pérot tunable filter spectrometers and a digital micro-mirror device were employed to achieve spectral and spatial resolution, respectively. The available spectral range from 1500 to 2200 nm covers molecular overtone vibrations enabling chemical identification. Hyperspectral images of different adhesives deposited on a textile were recorded revealing their chemical composition. Furthermore, spectrally resolved near-infrared images with compression rates up to 90% are presented. The approach of single pixel imaging illustrates a promising technology for the infrared spectral range superior to conventionally used costly focal plane arrays.