  A bound state in the continuum (BIC) is a localized state of an open
structure with access to radiation channels, yet it remains highly confined
with, in theory, infinite lifetime and quality factor. There have been many
realizations of such exceptional states in dielectric systems without loss.
However, realizing BICs in systems with losses such as plasmonics remains a
challenge. In this Letter, we explore the possibility of realizing BICs in a
hybrid plasmonic-photonic structure consisting of a plasmonic grating coupled
to a dielectric optical waveguide. The plasmonic-photonic system supports two
distinct groups of BICs: symmetry protected BICs at the {\Gamma}-point and
off-{\Gamma} Friedrich-Wintgen BICs. The photonic waveguide modes are strongly
coupled to the gap plasmons in the grating leading to an avoided crossing
behavior with a high value of Rabi splitting of 150 meV. Moreover, we show that
the strong coupling significantly alters the band diagram of the hybrid system
revealing opportunities for supporting stopped light at an off-{\Gamma} wide
angular span.
