We consider a model of weakly coupled quantum Ising chains. We describe the phase diagram of such a model and study the dynamical magnetic susceptibility by means of Bethe ansatz and the Random Phase Approximation applied to the inter-chain exchange. We argue that some of the beautiful physics of the quantum Ising chain in a magnetic field survives in the ordered state of the quasi-one-dimensional model and can be observed experimentally by means of neutron scattering.