Europa, the ice-covered satellite of Jupiter, is currently the most favorable site for the search of extraterrestrial life. Hydrothermal vents on the Earth's sea floor have been found to sustain life forms that can live without solar energy. Similar possible volcanic activity on Europa, caused by its interaction with Jupiter and the other Galilean satellites, makes this Jovian moon the best target for identifying a separate evolutionary line. This search addresses the main problem remaining in astrobiology, namely, the quest for discrete, or 'parallel' evolutionary lines in the universe. We explore ideas related to Europa's possible biological activity, particularly its likely degree of evolution. We have conjectured that evolution may have occurred in Europa and that the experimental test of such a conjecture is feasible. A lander space craft capable of penetrating the Europan surface ice-layer does not seem beyond present technological capabilities. Although difficult instrumentation issues are involved, we have initiated the discussion of what would seem to be a reasonable biological experiment. The possibility of detecting biomolecules on the ice surface of Europa has recently been made by others. A possible mechanism for bringing biomolecules to Europa's surface will be critically reviewed.