  Inelastic neutron scattering study on the spin-chain compound Sr$_3$NiIrO$_6$
reveals gapped quasi-1D magnetic excitations. The observed one-magnon band
between 29.5 and 39 meV consists of magnon modes of the Ni$^{2+}$ ions. The
fitting of the spin wave spectrum reveals strongly coupled Ising-like chains
along the $c$-axis that are weakly coupled into a frustrated triangular lattice
in the $ab$-plane. The magnetic excitations survive up to 200 K well above the
magnetic ordering temperature of $T_N \sim 75$ K, also indicating a quasi-1D
nature of the magnetic interactions in Sr$_3$NiIrO$_6$. Our microscopic model
is in good agreement with ab initio electronic structure calculations and
explains the giant spin flip field observed in bulk magnetization measurements.
