Thesis (Ph.D.) - Indiana University, Physics, 2012We present a first-of-its-kind confirmation that the most massive known elementary particle obeys the special theory of relativity. Lorentz symmetry is a fundamental aspect of special relativity which posits that the laws of physics are invariant regardless of the orientation and velocity of the reference frame in which they are measured. Because this symmetry is a fundamental tenet of physics, it is important to test its validity in all processes. We quantify violation of this symmetry using the Standard-Model Extension framework, which predicts the effects that Lorentz violation would have on elementary particles and their interactions. The top quark is the most massive known elementary particle and has remained inaccessible to tests of Lorentz invariance until now. This model predicts a dependence of the production cross section for top and antitop quark pairs on sidereal time as the orientation of the experiment in which these events are produced changes with the rotation of the Earth. Using data collected with the D0 detector at the Fermilab Tevatron Collider, we search for violation of Lorentz invariance in events involving the production of a top and antitop quark pair. Within the experimental precision, we find no evidence for such a violation and set upper limits on parameters describing its possible strength within the Standard-Model Extension. We also investigate the prospects for extending this analysis using the ATLAS detector at the Large Hadron Collider which, because of the higher rate of events containing a top and antitop quark pair at that experiment, has the potential to improve the limits presented here.