A search for sidereal variations in the frequency difference between co-located 129 Xe and 3 He Zeeman masers sets the most stringent limit to date on leading-order Lorentz and CPT violation involving the neutron, consistent with no effect at the level of 10 231 GeV. PACS numbers: 06.30.Ft, 11.30.Cp, 11.30.Er, 84.40.Ik Lorentz symmetry is a fundamental feature of modern descriptions of nature, including both the standard model of particle physics and general relativity. However, these realistic theories are believed to be the low-energy limit of a single fundamental theory at the Planck scale. Even if the underlying theory is Lorentz invariant, spontaneous symmetry breaking might result in small apparent violations of Lorentz invariance at an observable level. Experimental investigations of the validity of Lorentz symmetry therefore provide valuable tests of the framework of modern theoretical physics.Clock-comparison experiments [1-6] serve as sensitive probes of rotation invariance and hence of Lorentz symmetry, essentially by bounding the frequency variation of a clock as its orientation changes. In practice, the most precise limits are obtained by comparing the frequencies of two different co-located clocks as they rotate with the Earth. Typically, the clocks are electromagnetic signals emitted or absorbed on hyperfine or Zeeman transitions.Here, we report on a search for sidereal variations in the frequency of co-located 129 Xe and 3 He masers, both operating on nuclear spin-1͞2 Zeeman transitions. In the context of a general standard-model extension allowing for the possibility of Lorentz and CPT violation [7,8], the 129 Xe͞ 3 He-maser experiment sets the most stringent limit to date on leading-order Lorentz and CPT violation of the neutron: about 10 231 GeV, or more than 6 times better than the best previous measurements [9].The standard-model extension used to interpret this experiment emerges from any underlying theory that reduces at low energy to the standard model and contains spontaneous Lorentz violation [10]. For example, this might occur in string theory [11]. The standard-model extension maintains theoretically desirable properties of the usual standard model [8] [22,23]. A reanalysis by Adelberger, Gundlach, Heckel, and co-workers of existing data from a spin-polarized torsion-pendulum experiment [24,25] sets the most stringent bound to date on Lorentz and CPT violation of the electron, at about 10 228 GeV [26]. A recent Lorentzsymmetry test using hydrogen masers searched for hydrogen Zeeman-frequency sidereal variations, placing a bound on Lorentz violation at the level of 10 227 GeV [27]. Together with the results of Ref. [26], this implies an improved clean limit of 10 227 GeV on Lorentz-violating couplings involving the proton. Also, the KTeV experiment at Fermilab and the OPAL and DELPHI collaborations at CERN have constrained possible Lorentz-and CPT-violating effects in the K and B d systems [28,29].The design and operation of the two-species 129 Xe͞ 3 He maser has been discussed in r...