We report ^{51}V NMR and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo_{2}V_{2}O_{8} under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxation rate above the Néel temperatures unveils a 1D quantum critical point (QCP) at H_{c}^{1D}≈4.7 T, which is masked by the 3D magnetic order. With the aid of accurate analytical analysis and numerical calculations, we show that the zone center INS spectrum at H_{c}^{1D} is precisely described by the pattern of the 1D quantum Ising model in a magnetic field, a class of universality described in terms of the exceptional E_{8} Lie algebra. These excitations are nondiffusive over a certain field range when the system is away from the 1D QCP. Our results provide an unambiguous experimental realization of the massive E_{8} phase in the compound, and open a new experimental route for exploring the dynamics of quantum integrable systems as well as physics beyond integrability.
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