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\font\rma=cmr8 An unresolved compression front ($<1'$, seen in all four bands of high resolution IRAS data) surrounding the Rosette Nebula was mapped in the $^{13}$CO J=1$\rightarrow$0 transition. This compression front results from the thermal expansion of the H\thinspace{\rma II} region into the parent molecular cloud. High spectral (0.68 km s$^{-1}$) and spatial (48$''$) resolution molecular data were obtained using the Five College Radio Astronomy Observatory (FCRAO) QUARRY receivers. Approximately 6500, low noise ($\Delta$T$_{\rm rms}$ = 0.1 -- 0.2 K) spectra were observed over a 1.5 square degree area. The intensity maps show several relatively dense clumps surrounding only a portion of the optical nebula along with more tenuous emission. With a few exceptions, most of these dense clumps have associated IRAS point sources. The kinematics and density structure of these clumps are presented.
