Polarized and unpolarized inelastic neutron scattering is used to study Haldane-gap excitations in the mixed-spin linear-chain antiferromagnet Nd2BaNiO5. The longitudinal mode, polarized along the direction of ordered moments, is observed for the first time. The model of isolated Haldane chains in a static staggered exchange field, that is known to work very well for static properties and transverse spin excitations in R2BaNiO5 compounds, fails to explain new results for the longitudinal spin gap. 75.30.Ds,75.50.Ee,75.40.Gb The novel quantum-disordered ground state and the famous Haldane gap in the magnetic excitation spectrum [1] have kept integer-spin one-dimensional (1-D) Heisenberg antiferromagnets (AF) at the center of attention of condensed matter physicists for almost 2 decades. Among the more recent developments are studies of such systems in external magnetic fields (comprehensive bibliography can be found in Refs. [2][3][4]). As the uniform magnetic field H is increased, the Haldane triplet splits linearly with H, one of the three excitations decreases in energy and eventually softens at some critical field H c . The result is a transition to a radically new phase with long-range magnetic order (see for example Refs. [5,6]) The effect of strong a staggered field H π , to which the Haldane chain is most susceptible, is expected to be no less dramatic. According to recent theoretical results [7,8] and numerical simulations [9], all three Haldane gap energies increase quadratically with H π . The degeneracy of the Haldane triplet is removed: for the excitation polarized along the direction of induced moments (longitudinal mode) the gap increases three times more rapidly than for the two transverse modes. The longitudinal mode is of particular interest, as it is a purely quantum feature, totally absent in the classical spin wave theory that predicts a pair of transverse order-parameter excitations (magnons).The discovery of coexistence of Haldane gap excitations and magnetic long-range order in R 2 BaNiO 5 (R=magnetic rare earth) compounds [10-14] presented a unique opportunity to investigate experimentally the effect of a strong staggered field on Haldane spin chain. In R 2 BaNiO 5 the initially quantum-disordered AF S = 1 Ni 2+ -chains become subject to an effective staggered exchange field produced by the R-sublattice, when the latter orders magnetically at low temperatures. The magnitude of this field can be tuned by varying the temperature and thereby the ordered moment on the R [8,9]. Surprisingly, the splitting of the Haldane triplet could never be found. In fact, no clear evidence for the very existence of the longitudinal mode in R 2 BaNiO 5 has been obtained: all the measured staggered field dependencies of the Haldane gap energies are in quantitative agreement with calculations for transverse excitations in isolated chains [8,13,7,9]. The present paper is aimed at resolving this mystery. We report the first direct experimental observations of the longitudinal mode in a R 2 BaNiO 5 compound u...