While Europa has emerged as a leading candidate for harboring extraterrestrial life, the apparent lack of a source of free energy for sustaining living systems has been argued. In this theoretical analysis, we have quantified the amount of energy that could in principle be obtained from chemical cycling, heat, osmotic gradients, kinetic motion, magnetic fields, and gravity in Europa's subsurface ocean. Using reasonable assumptions based on known organisms on Earth, our calculations suggest that chemical oxidation-reduction cycles in Europa's subsurface ocean could support life. Osmotic and thermal gradients, as well as the kinetic energy of convection currents, also represent plausible alternative sources of energy for living systems at Europa. Organisms thriving on these gradients could interact with each other to form the complex energy cycling necessary for establishing a stable ecosystem.