We report on the demonstration of three-dimensional optical trapping inside the core of a hollow-core microstructured optical fiber specifically designed and fabricated for this purpose. Optical trapping was achieved by means of an external tweezers beam incident transversely on the fiber and focused through the fiber cladding. Trapping was achieved for a range of particle sizes from 1 to 5 µm, and manipulation of the particles in three-dimensions through the entire cross-section of the fiber core was demonstrated. Spectroscopy was also performed on single fluorescent particles, with the fluorescence captured and guided in the fiber core. Video tracking methods allowed the optical traps to be characterized and photobleaching of single particles was also observed and characterized.