Rational speculation about biological evolution on other worlds is one of the outstanding challenges in astrobiology. With the growing confirmation that multiplanetary systems abound in the universe, the prospect that life occurs redundantly throughout the cosmos is gaining widespread support. Given the enormous number of possible abodes for life likely to be discovered on an ongoing basis, the prospect that life could have evolved into complex, macro-organismic communities in at least some cases merits consideration. Toward that end, we here propose a Biological Complexity Index (BCI), designed to provide a quantitative estimate of the relative probability that complex, macro-organismic life forms could have emerged on other worlds. The BCI ranks planets and moons by basic, first-order characteristics detectable with available technology. By our calculation only 11 (~1.7%) of the extrasolar planets known to date have a BCI above that of Europa; but by extrapolation, the total of such planets could exceed 100 million in our galaxy alone. This is the first quantitative assessment of the plausibility of complex life throughout the universe based on empirical data. It supports the view that the evolution of complex life on other worlds is rare in frequency but large in absolute number.