InAs quantum dot arrays are obtained on GaAs nanowire facets by molecular beam epitaxy. The GaAs nanowires are first grown by the gallium-assisted catalyst-free method. Decoration of the nanowire facets with InAs quantum dots is achieved only when the facets are capped with an ultrathin AlAs layer, as demonstrated by atomic force, high-resolution electron microscopy, and energy-dispersive X-ray spectroscopy line scans. The excitation of single and double excitons in the quantum dots are demonstrated by low-temperature photoluminescence spectroscopy realized on the single nanowires. This new type of heterostructures opens a new avenue to the fabrication of highly efficient single-photon sources, novel quantum optics experiments, as well as the realization of intermediate-band nanowire solar cells for third-generation photovoltaics.