There has been significant interest recently in the development of materials that utilize the kinetic properties of self-associating groups, which can be tuned to manipulate dynamics and control mechanical, optical, and rheological properties. Here we describe the single-chain behavior of self-associating polymers in solution, using results from both simulation and theory. We use Brownian dynamics simulations with monomers that can reversibly associate using Bell model-based reaction kinetics. A straightforward two-state model is considered, and associations are exclusive; however, generalizations beyond these behaviors are briefly considered in the theory. We demonstrate that, even for a Theta-polymer, the inclusion of self-associations can drive the polymer into an equilibrium structure that resembles a collapsed polymer globule. The dynamic behavior of these polymers exhibits two regimes, with Rouse-dominated time scales when binding reactions have low energetic barriers and binder-dominated time scales when binding reactions have large energetic barriers. These results have implications in a diverse array of applications ranging from supramolecular chemistry to stimuli responsive materials to biological polymer dynamics.