A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.” Such an extraordinary feature may appear unattainable in any realistic and simple theory of physics. In this paper, I propose a definition of strong determinism and contrast (...) it with those of standard determinism and super-determinism. Next, I discuss its consequences for explanation, causation, prediction, fundamental properties, free will, and modality. Finally, I present the first example of a realistic, simple, and strongly deterministic physical theory--the Everettian Wentaculus. As a consequence of physical laws, the history of the Everettian multiverse could not have been different. If the Everettian Wentaculus is empirically equivalent to other quantum theories, we can never empirically find out whether or not our world is strongly deterministic. Even if strong determinism fails to be true, it is closer to the actual world than we have presumed, with implications for some of the central topics in philosophy and foundations of physics. (shrink)