  We study the isotropic XY quantum spin chain with a time-periodic transverse
magnetic field acting on a single site. The asymptotic problem can be mapped
into a highly resonant Floquet-Schr\"odinger equation, for which, under a
diophantine-like assumption on the frequency, we show the existence of a
periodic solution. The proof is based on a KAM-type renormalisation. This in
turn implies the state of the quantum spin chain to be asymptotically a
periodic function synchronised with the forcing also at low frequencies.
