Over the past century, stellar structure and evolution models (SSEMs) have become foundational to many areas of astrophysics - from exoplanets to cosmology. Thus, the accuracy of SSEMs continues to be a topic of intense interest with nearly continuous refinements to numerical methods, empirical inputs, and parameterizations of hydro- and magnetohydrodynamic effects. The accuracy of these models, however, may be fundamentally limited by dynamical chaos - the exponential growth of uncertainty in deterministic systems. Using the Modules for Experiments in Stellar Astrophysics (MESA) code, we show that indeed SSEMs can display dynamical chaos for rotating solar-like main sequence stars. The combination of coupled boundary-value and initial-value solves leads to an exponential growth in model uncertainty on relatively short timescales, causing models initially different by less than 1 part in 108 to show exponential divergence. We report initial work on the implications of this chaos, including fundamental uncertainties in the calculated stellar radii, effective temperature, and depth of the outer convective layer.