  We discuss spectral properties of a charged quantum particle confined to a
chain graph consisting of an infinite array of rings under influence of a
magnetic field assuming a $\delta$-coupling at the points where the rings
touch. We start with the situation when the system has a translational symmetry
and analyze spectral consequences of perturbations of various kind, such as a
local change of the magnetic field, of the coupling constant, or of a ring
circumference. A particular attention is paid to weak perturbations, both local
and periodic; for the latter we prove a version of Saxon-Hutner conjecture.
