  We present the first measurement for helium atoms of the tune-out wavelength
at which the atomic polarizability vanishes. We utilise 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 electro-dynamic (QED) effects.
This provides motivation for more detailed theoretical investigations to test
QED.
