The 2 ^{3}S-2 ^{3}P transition of ^{4}He was measured by comb-linked laser spectroscopy using a transverse-cooled atomic beam. The centroid frequency was determined to be 276 736 495 600.0(1.4) kHz, with a fractional uncertainty of 5.1×10^{-12}. This value is not only more accurate but also differs by as much as -49.5 kHz (20σ) from the previous result given by [Cancio Pastor et al., Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001; Cancio Pastor et al.Phys. Rev. Lett.97, 139903(E) (2006)10.1103/PhysRevLett.97.139903; Cancio Pastor et al.Phys. Rev. Lett.108, 143001 (2012)10.1103/PhysRevLett.108.143001]. In combination with ongoing theoretical calculations, this work may allow the most accurate determination of the nuclear charge radius of helium.