Photodetectors operating in the ultraviolet (UV) play a pivotal role in applications such as ozone monitoring and biosensing. One key factor to successfully implementing such photodetectors is that they must be solar-blind to avoid detecting ambient visible and infrared light. Unfortunately, UV photodetectors based on silicon and other typical semiconductors are not natively solar-blind, since their band gap energies are in the visible range. Hexagonal boron nitride (h-BN) is an example of a wide band gap semiconductor which shows promise for use as the absorbing medium in a UV photodetector device, since its band gap is wide enough to make it inherently insensitive to light in the visible range and above. Here we report on the fabrication and characterization of a graphene-h-BN-heterostructure photodetector which utilizes a vertical geometry, in principle allowing for highly scalable production. We find that our device shows a finite photoresponse to illumination by a 254 nm light source, but not to a 365 nm source, thus suggesting that our device is solar-blind.