Starting with intensity requirements for producing efficient ablation thrust, then applying orbital mechanics and taking beam transport into account, we have determined the laser pulse energy and the number of pulses required for removing orbital debris. Our calculations show that a ground-based, diode-pumped, gas-cooled multi-slab laser, that uses only modest extensions of existing technology, would be capable of removing most small debris from low-earth orbit, when used with a 3-m-diameter beam director. Such a laser would also be capable of moving large debris into orbits that avoid high-value satellites and of even removing large debris from orbit, by illuminating the debris over several encounters. The laser design we propose uses diode-pumped, Nd:glass, gas-cooled amplifiers with 25-cm square apertures. When operating at the laser fundamental wavelength of 1054 nm, each beamline would produce similar to 8kJ / 4ns pulses at 15 Hz. Two such beamlines, combined using established polarization-combining methods, would be sufficient for orbital debris cleaning. Alternatively, when operating at the second harmonic of 527 nm, each beamline would produce similar to 7 kJ / 4 ns pulses. Due to reduced beam divergence and a smaller beam diameter at the debris, a single harmonically-converted beamline can be useful. We estimate that the first-of-a-kind beamline could be deployed within 4-5 years of project start at a cost of $100-$150M. Later beamlines would require less development and engineering costs and would have substantially lower overall cost.