This work studies the guided localized electromagnetic waves propagating along finite and infinite chains of parallel thin resonant wires periodically arranged over an interface of a dielectric half-space. Both issues of guided wave propagation in an infinite chain and resonant excitation of hybridized eigenmodes of a finite chain are solved analytically and numerically. The effect of changing the modes' resonant frequency order is observed as the chain approaches the interface closer than its periodicity staying inside the dielectric. This effect, called mode hopping, has been directly demonstrated by solving the problem of a finite chain excited by a plane wave using Pocklington's system of integral equations. Moreover, the effect was further related to the dispersion properties of the corresponding infinite array. The analytically described mode-hopping effect was verified numerically and experimentally.