We present the first measurement for helium atoms of the tune-out wavelength at which the atomic polarizability vanishes. We utilize a novel, highly sensitive technique for precisely measuring the effect of variations in the trapping potential of confined metastable (2^{3}S_{1}) helium atoms illuminated by a perturbing laser light field. The measured tune-out wavelength of 413.0938(9_{stat})(20_{syst}) nm compares well with the value predicted by a theoretical calculation [413.02(9) nm] which is sensitive to finite nuclear mass, relativistic, and quantum electrodynamic effects. This provides motivation for more detailed theoretical investigations to test quantum electrodynamics.
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