The root-mean-square (rms) nuclear charge radius of 8He, the most neutron-rich of all particle-stable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of 6He was measured to be 2.068(11) fm, in excellent agreement with a previous result. The significant reduction in charge radius from 6He to 8He is an indication of the change in the correlations of the excess neutrons and is consistent with the 8He 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.