A single, trapped and ultracold molecular hydrogen ion is an attractive quantum system for exploring various aspects of fundamental physics, such as the determination of fundamental constants and testing their time-independence. Here we demonstrate, for the first time, controlled loading, sympathetic cooling, mass spectrometric identification, and vibrational excitation of ultracold single HD (Formula presented.) ions trapped in a tightly confining radiofrequency trap using single laser-cooled Be (Formula presented.) ions for sympathetic cooling. The apparatus can be used also for preparing other single ions, both lighter and heavier than the coolant ion.