Coherent-population trapping, heretofore realized in closed systems, i
s also possible in highly degenerate open molecular systems. We consid
er a rovibrational molecular transition, where the ground magnetic m-s
ublevels are coupled to the corresponding upper states, and are theref
ore expected to be emptied after a few lifetimes. We show that upon ex
citation by elliptically polarized light, the population remains trapp
ed in a coherent superposition of ground-state sublevels which does no
t interact further with the exciting light. Unlike the simple cases of
linearly and circularly polarized light and of a closed three-level s
ystem (i.e. atoms), here the trapping level is not the one with \m\ =
0, J, but rather a combination of several states, which depends on the
ellipticity of the exciting light.