  $\alpha$-RuCl$_{3}$ is a major candidate for the realization of the Kitaev
quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures
indicates deviations from the Kitaev model. We have quantified the spin
Hamiltonian of $\alpha$-RuCl$_{3}$ by a resonant inelastic x-ray scattering
study at the Ru $L_{3}$ absorption edge. In the paramagnetic state, the
quasi-elastic intensity of magnetic excitations has a broad maximum around the
zone center without any local maxima at the zigzag magnetic Bragg wavevectors.
This finding implies that the zigzag order is fragile and readily destabilized
by competing ferromagnetic correlations. The classical ground state of the
experimentally determined Hamiltonian is actually ferromagnetic. The zigzag
state is stabilized via a quantum "order by disorder" mechanism, leaving
ferromagnetism -- along with the Kitaev spin liquid -- as energetically
proximate metastable states. The three closely competing states and their
collective excitations hold the key to the theoretical understanding of the
unusual properties of $\alpha$-RuCl$_{3}$ in magnetic fields.
