Early in the last century, Robert Millikan developed a precise method of determining the electric charge carried by oil droplets. Using a microscope and a small incandescent lamp, he observed the fall of charged droplets under the influence of an electric field inside a small observation chamber. In so doing, Millikan demonstrated the existence of a fundamental unit of electric charge, and established its quantization. Now renowned as one of the most famous experiments of 20th-century physics, Millikan's oil-drop experiment has been reproduced with more or less success in most, if not all, high school and university physics classes. This has encouraged many improvements of the apparatus, now making this experiment much more accurate and easier to realize for advanced students. However, the required apparatus remains rather expensive, and for introductory college or high school students the experiment is still quite difficult to conduct. As an alternative to the traditional setup, a realistic computer-based simulator to replicate the Millikan oil-drop experiment has been developed. Using this software, students are able to undertake a complete experiment, obtain an accurate set of results, and thus gain a better understanding of the original experiment and its historical importance. (Contains 7 figures and 2 tables.)