Measurement of the Target-Normal Single-Spin Asymmetry in Deep-Inelastic Scattering from the Reaction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>He</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mm

We report the first measurement of the target-normal single-spin asymmetry in deep-inelastic scattering from the inclusive reaction ^3He^↑ (e,e′) X on a polarized ^3He gas target. Assuming time-reversal invariance, this asymmetry is strictly zero in the Born approximation but can be nonzero if two-photon-exchange contributions are included. The experiment, conducted at Jefferson Lab using a 5.89 GeV electron beam, covers a range of 1.7 2 GeV, which is nonzero at the 2.89σ level. Our measured asymmetry agrees both in sign and magnitude with a two-photon-exchange model prediction that uses input from the Sivers transverse momentum distribution obtained from semi-inclusive deep-inelastic scattering.