Contamination Crew by Alan E. Nourse, Science Fiction, Adventure

The entire population of Mauki was found to be suffering from a mass psychotic delusion of rather spectacular proportions: namely, that they and their entire planet were in imminent danger of being devoured, in toto, by an indestructible non-humanoid creature which they called a hlorg . . . Orders are orders! The creature had to be killed. But just how does one destroy the indestructible?