  We present a grid-based implementation of the time-dependent
configuration-interaction singles method suitable for computing the
strong-field ionization of small gas-phase molecules. After outlining the
general equations of motion used in our treatment of this method, we present
example calculations of strong-field ionization of helium, lithium hydride,
water, and ethylene that demonstrate the utility of our implementation. The
following companion paper specializes to the case of spherical symmetry, which
is applied to various atoms.
