  We develop a detailed chemical model for the starless cores of strongly
magnetized molecular clouds, with the ambipolar diffusion-driven dynamic
evolution of the clouds coupled to the chemistry through ion abundances. We
concentrate on two representative model clouds in this initial study, one with
magnetic fields and the other without. The model predictions on the peak values
and spatial distributions of the column densities of CO, CCS, N$_2$H$^+$ and
HCO$^+$ are compared with those observationally inferred for the well-studied
starless core L1544, which is thought to be on the verge of star formation. We
find that the magnetic model, in which the cloud is magnetically supported for
several million years before collapsing dynamically, provides a reasonable
overall fit to the available data on L1544; the fit is significantly worse for
the non-magnetic model, in which the cloud collapses promptly. The observed
large peak column density for N$_2$H$^+$ and clear central depression for CCS
favor the magnetically-retarded collapse over the free-fall collapse. A
relatively high abundance of CCS is found in the magnetic model, resulting most
likely from an interplay of depletion and late-time hydrocarbon chemistry
enhanced by CO depletion. These initial results lend some support to the
standard picture of dense core formation in strongly magnetized clouds through
ambipolar diffusion. They are at variance with those of Aikawa et al. (2001)
who considered a set of models somewhat different from ours and preferred one
in which the cloud collapses more or less freely for L1544.
