With regards to the real-world, the NOAA says that some deep-sea crabs have low-level UV sensitivity in certain pigments. This would seem to indicate that creatures there may emit UV light - which is exactly what you're looking for - potentially as a form of communication1:
In addition, data obtained on previous OE-funded expeditions indicate that the deep-sea benthos may produce novel, short wavelength bioluminescence. During Deep Scope 2005, we discovered that several species of the deep-sea crabs (figure 2b) have an ultraviolet (UV)-sensitive visual pigment in addition to a blue-sensitive one. In their dim light environment, sacrificing room in their eyes for a UV visual pigment suggests that UV sensitivity plays an important role in their ecology. Just as unusual UV sensitivity in several deep-sea pelagic species has been linked to bioluminescence, we suspect that UV sensitivity may also function to see as-yet-undiscovered short wavelength bioluminescence from benthic organisms. UV bioluminescence in the benthos may be a novel private channel of communication, allowing these animals to find their preferred habitat.
Additionally, Photophysiology: Action of Light on Animals and Microorganisms; Photobiochemical Mechanisms; Bioluminescence cites the findings of Cormier and Eckroade (1962) of evidence of bioluminescent emission in the UV wavelengths in three species of the Renilla genus (commonly called sea pansies; these effects were later investigated by Hart et al. (1979)). It's important to note that the emission of photons in UV wavelengths is only due to a "tailing off" of the spectral energy distribution in the bioluminescence of these species.
Feasibility is more complicated. The mechanism2 is
as mediated by the enzyme luciferase using one of the luciferin pigments. Essentially, the luciferin changes from an excited state to a ground state. Now, we can postulate the existence of a luciferin with an energy difference between these two states exactly right to produce one or more UV photons; in fact, Biology: The Unity and Diversity of Life claims that "some even emit ultraviolet or infrared light" but doesn't specify which luciferins it is referencing.
1 UV light is used for communication in other animals; see Sensory Ecology, Behavior, and Evolution.
2 Note that this is not the only reaction mechanism for bioluminescence.