Violation of Lorentz invariance is searched for using top quark pair (tt) production in proton-proton collisions at the LHC, at a center-of-mass energy of sqrt(s) = 13 TeV. Events containing one electron and one muon collected with the CMS detector are analyzed in a data sample corresponding to an integrated luminosity of 77.8 fb−1. A measurement of the normalized differential cross section for tt production as a function of sidereal time is performed. Potential violation of Lorentz invariance is introduced as an extension of the standard model, with an effective field theory predicting the modulation of the tt cross section with sidereal time. Bounds on Lorentz-violating couplings are extracted, and found to be compatible with the SM predictions assuming Lorentz invariance with an absolute precision of 1 × 10−3 to 8 × 10−3. This search can be interpreted as a precision test of special relativity with top quarks, improving precision by up to two orders of magnitude over a previous such measurement at the Tevatron.