The fundamental constants (FCs) of physics are promoted to dynamic quantities in modern theories. So far most of the literature focused on small fractional variations in the values of FCs. In this paper, we investigate the novel regime of extreme but transient variations of FCs. We focus on the speed of light (c) and show that its variation can dramatically change the electronic structure and chemistry of atoms and molecules. These changes are induced by increased relativistic effects when c is reduced from its nominal value. To model these changes, we solve the fully relativistic Dirac equation at different values of c. We show that at extreme variations of c, the periodic table is truncated, the nominal ground states of atoms can change, water fails to serve as a universal solvent, and the ammonia molecule becomes planar.