In this thesis I treat success in explicating probabilistic laws of nature (e.g., laws of radioactive decay) as a criterion of adequacy for a metaphysics of laws. I devote a chapter of analysis to each of the three best known theories of laws: the best systems analysis, contingent necessitation, and dispositional essentialism. I treat the problem of undermining that David Lewis identified in his theory of chance as a challenge that any metaphysical theory of probabilistic laws must overcome. I argue that dispositional essentialism explicates probabilistic laws while the other two theories fail to do so. Lewis's best systems analysis explicates probabilistic laws only with a solution to the problem of undermining. Michael Thau's solution was met with Lewis's approval. I argue that Thau's solution is ad hoc and renders impossible the fit of best systems with probabilistic laws to indeterministic worlds. Bas van Fraassen argued that David Armstrong's theory of contingent necessitation is totally incapable of explicating probabilistic laws of nature. I argue that Armstrong is able to respond to some of van Fraassen's arguments, but not to the extent of rehabilitating his theory. I also argue that Armstrong's theory of probabilistic laws suffers from the problem of undermining. This result adds to the widely held suspicion that Armstrong's theory is a version of a regularity theory of laws. With propensities grounding probabilistic laws of nature, the problem of undermining does not arise for dispositional essentialism, because all nomically possible futures are compatible with the propensities instantiated in the world. I conclude that dispositional essentialism explicates probabilistic laws of nature better than Lewis's and Armstrong's theories do. Since probabilistic laws are ubiquitous in contemporary physics, I conclude that dispositional essentialism furnishes a better metaphysics of laws than Lewis's and Armstrong's theories do. / Thesis / Doctor of Philosophy (PhD)