Understanding the nature of the glass transition-the dramatic slowing of dynamics and eventual emergence of a disordered solid from a cooling liquid-is a fundamental challenge in physical science. A central characteristic of glass-forming liquids is a non-exponential main relaxation process. The extent of deviation from exponential relaxation typically becomes more pronounced on cooling. Theories that predict a growth of spatially heterogeneous dynamics as temperature is lowered can explain these observations. In apparent contradiction to these theories, however, some experiments suggest that certain substances-notably including the intensely studied molecular glass-former ortho-terphenyl (OTP)-have a main relaxation process whose shape is essentially temperature independent, even though other observables predicted to be correlated with the degree of dynamical heterogeneity are temperature dependent. Here we report the first simulations based on an atomistic model of OTP that reach equilibrium at temperatures well into the supercooled regime. We first show that the results of these simulations are in reasonable quantitative agreement with experimental data for several basic properties over a wide range of temperatures. We then focus on rotational relaxation, finding nearly exponential behavior at high temperatures with clearly increasing deviations as temperature is lowered. The much weaker temperature dependence observed in light-scattering experiments also emerges from the same simulation data when we calculate correlation functions similar to those probed experimentally; this highlights the diversity of temperature dependencies that can be obtained with different probes. Further analysis suggests that the temperature insensitivity observed in the light-scattering experiments stems from the dependence of these measurements on internal as well as rotational molecular motion. Within the temperature range of our OTP simulations, our results strongly suggest that this archetypal glass-former behaves as anticipated by theories of the glass transition that predict increasing non-exponentiality with cooling, and our simulations thus strengthen the evidence supporting such theories.