  We propose a model of a heterogeneous glass forming liquid and compute the
low-temperature behavior of a tagged molecule moving within it. This model
exhibits stretched-exponential decay of the wavenumber-dependent, self
intermediate scattering function in the limit of long times. At temperatures
close to the glass transition, where the heterogeneities are much larger in
extent than the molecular spacing, the time dependence of the scattering
function crosses over from stretched-exponential decay with an index $b=1/2$ at
large wave numbers to normal, diffusive behavior with $b = 1$ at small
wavenumbers. There is a clear separation between early-stage, cage-breaking
$\beta$ relaxation and late-stage $\alpha$ relaxation. The spatial
representation of the scattering function exhibits an anomalously broad
exponential (non-Gaussian) tail for sufficiently large values of the molecular
displacement at all finite times.
