At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. From the latter observational fact, this paper seeks to place upper limits on the probability of an interstellar civilization arising on a habitable planet in its stellar system, using a percolation model to simulate the progress of such a hypothetical civilization's colonization efforts in the local Solar neighbourhood. To be as realistic as possible, the actual physical positions and characteristics of all stars within 40 parsecs of the Solar System are used as possible colony sites in the percolation process. If an interstellar civilization is very likely to have such colonization programmes, and they can travel over large distances, then the upper bound on the likelihood of such a species arising per habitable world is of the order of 10−3; on the other hand, if civilizations are not prone to colonize their neighbours, or do not travel very far, then the upper limiting probability is much larger, even of order one.