  We propose a new cosmological model with a time-dependent cosmological
constant ($\Lambda\propto 1/t^2$), which starting at the Planck time as
$\Lambda_{Pl}\sim M^2_{Pl}$, evolves to the present-day allowed value of
$\Lambda_0\sim10^{-120}M^2_{Pl}$. This scenario is supported by non-critical
string theory considerations. We compute the age of the Universe and the
time-dependence of the scale factor in this model, and find general agreement
with recent determinations of the Hubble parameter for substantial values of
$\Omega_{\rm \Lambda}$. This effectively low-density open Universe model
differs from the traditional cosmological constant model, and has observable
implications for particle physics and cosmology.
