We refine sequential equilibrium in signaling games by incorporating natural language in the form of meaningful cheap talk directly into the theory. Because literal meaning can be overridden by equilibrium usage, the import of natural language in games must stem in part from conventions about how literal meaning interacts with off-path beliefs. Our main result shows that a simple and intuitive convention together with a rich language has surprising refinement power, eliminating all equilibria except those that are stable in the sense of Kohlberg and Mertens (1986). Moreover, even with a very coarse language, the same convention eliminates, in particular, all equilibria that fail to satisfy Cho and Kreps’ (1987) never a weak best reply criterion.