We report the structure of isolated biomolecules, uracil and guanine, demonstrating the capability of a newly developed electron diffraction apparatus augmented with surface-assisted IR laser desorption. This UED-4 apparatus provides a pulsed, dense molecular beam, which is stable for many hours and possibly days. From the diffraction patterns, it is evident that the plume composition is chemically pure, without detectable background from ions, fragmentation products, or molecular aggregates. The vibrational temperature deduced is indeed lower than the translational temperature of the plume indicating that the molecules are intact on such short time scales. The structures of uracil and guanine were refined at the deduced internal temperatures, and we compare the results with those predicted by density functional theory. Such experimental capability opens the door for many other studies of the structure (and dynamics) of biomolecules.