We have grown epitaxial Cr-doped V$_2$O$_3$ thin films with Cr concentrations between $0$ and $20\%$ on $(0001)$-Al$_2$O$_3$ by oxygen-assisted molecular beam epitaxy. For the highly doped samples (> $3\%$), a regular and monotonous increase of the resistance with decreasing temperature is measured. Strikingly, in the low doping samples (between $1\%$ and $3\%$), a collapse of the insulating state is observed with a reduction of the low temperature resistivity by up to 5 orders of magnitude. A vacuum annealing at high temperature of the films recovers the low temperature insulating state for doping levels below $3\%$ and increases the room temperature resistivity towards the values of Cr-doped V$_2$O$_3$ single crystals. It is well-know that oxygen excess stabilizes a metallic state in V$_2$O$_3$ single crystals. Hence, we propose that Cr doping promotes oxygen excess in our films during deposition leading to the collapse of the low temperature insulating state at low Cr concentrations. These results suggest that slightly Cr-doped V$_2$O$_3$ films can be interesting candidates for field effect devices. ; Comment: 4 pages, 4 figures