  We present the concluding result from an Ives-Stilwell-type time dilation
experiment using 7Li+ ions confined at a velocity of beta = v/c = 0.338 in the
storage ring ESR at Darmstadt. A Lambda-type three-level system within the
hyperfine structure of the 7Li+ triplet S1-P2 line is driven by two laser beams
aligned parallel and antiparallel relative to the ion beam. The lasers' Doppler
shifted frequencies required for resonance are measured with an accuracy of < 4
ppb using optical-optical double resonance spectroscopy. This allows us to
verify the Special Relativity relation between the time dilation factor gamma
and the velocity beta to within 2.3 ppb at this velocity. The result, which is
singled out by a high boost velocity beta, is also interpreted within Lorentz
Invariance violating test theories.
