The exploration of icy moons and other icy regions such as permanently shadowed lunar craters, Martian polar caps or comets is of great scientific interest, as they might offer life-friendly environmental conditions or can serve as resource deposits for human exploration. In contrast to conventional melting probes, this work presents a laser ice drill, which drills a 6.15 mm diameter hole in the ice and drives the resulting gases and non-volatile additives from the bottom of the hole to the surface for analysis purposes. To demonstrate the concept, various types of ice with dust fraction up to 96.6 wt% were drilled in a laboratory setup. The tests were carried out at vacuum pressures in the 100 Pa range and ambient temperature. The drilling depth was simultaneously tracked with a laser rangefinder, so that a depth assignment of the ejected substances was possible. During the drilling tests, melting speeds of up to 1.7 m/h at 12.7 W laser power were achieved in pure granular ice and 1 m/h at 19.7 W in clear ice. In dusty ice, however, even higher drilling speeds were achieved without increasing the laser power. The melting rates of all drilling experiments are simulated in good agreement with a thermal model.