The eigenmodes analysis of Bloch modes in a chain of metallic nanowires (MNWs) provides a significant physical understanding about the light propagation phenomena involved in such structures. However, most of these analyses have been done above the light line in the dispersion relation, where the Bloch modes can only be excited with radiative modes. By making use of the Fourier modal method, in this paper we rigorously calculate the eigenmode and mode excitation of a chain of MNWs via the fundamental transverse magnetic (TM) mode of a dielectric waveguide. Quadrupolar and dipolar transversal Bloch modes were obtained in an MNW chain embedded in a dielectric material. These modes can be coupled efficiently with the fundamental TM mode of the waveguide. Since the eigenmodes supported by the integrated plasmonic structure exhibit strong localized surface plasmon (LSP) resonances, they could serve as a nanodevice for sensing applications. Also, the analysis opens a direction for novel nanostructures, potentially helpful for the efficient excitation of LSPs and strong field enhancement.