The root-mean-square (rms) nuclear charge radius of 8 He, the most neutron-rich of all particlestable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of 6 He was measured to be 2.068(11) fm, in excellent agreement with a previous result.The significant reduction in charge radius from 6 He to 8 He is an indication of the change in the correlations of the excess neutrons and is consistent with the 8 He neutron halo structure. The experiment was based on laser spectroscopy of individual helium atoms cooled and confined in a magneto-optical trap. Charge radii were extracted from the measured isotope shifts with the help of precision atomic theory calculations. * Electronic address: pmueller@anl.gov 1