  The ^{207}Pb^{19}F molecule possesses a pair of closely spaced levels of
opposite parity due to near cancelation of the omega-type doubling and magnetic
hyperfine interaction energy shifts [Alphei et al., Phys. Rev. A, 83, 040501
(2011)]. We calculate the dependence of the transition frequency between these
levels on the fine-structure constant (\alpha) and the ratio of the light quark
masses to the quantum chromodynamics scale (m_q/\Lambda_{QCD}), and find large
enhancement of the relative effects of the variation of these parameters. Note
that the effect of \alpha-variation appears mainly due to the significant
difference in the relativistic correction factors for the fine and hyperfine
structure. We hence suggest the ^{207}Pb^{19}F molecule as a candidate system
for investigating the possible temporal variation of the fundamental constants.
