  Polariton-based devices require materials where light-matter coupling under
ambient conditions exceeds losses, but our current selection of such materials
is limited. Here we measured the dispersion of polaritons formed by the $A$ and
$B$ excitons in thin MoS$_2$ slabs by imaging their optical near fields. We
combined fully tunable laser excitation in the visible with a scattering
near-field optical microscope to excite polaritons and image their optical near
fields. We obtained the properties of bulk MoS$_2$ from fits to the slab
dispersion. The in-plane excitons are in the strong regime of light-matter
coupling with a coupling strength ($40-100\,$meV) that exceeds their losses by
at least a factor of two. The coupling becomes comparable to the exciton
binding energy, which is known as very strong coupling. MoS$_2$ and other
transition metal dichalcogenides are excellent materials for future polariton
devices.
