  We investigate the cosmological dynamics of a class of supersymmetric
chameleon models coupled to cold dark matter fermions. Supergravity corrections
ensure that these models are efficiently screened in all astrophysical objects
of interest, however this does not preclude the enhancement of gravity on
linear cosmological scales. We analyse the background cosmology and solve the
modified equations for the growth of cold dark matter density perturbations in
closed form. Using this, we go on to derive the modified linear power spectrum
which is characterised by two scales, the horizon size at matter-radiation
equality and at the redshift when the chameleon reaches the minimum of its
effective potential. The model includes a cosmological constant in the form of
a Fayet-Illiopolous term, which emerges at late times due to the coupling of
the chameleon to two charged scalars. We examine the conditions under which
this leads to viable background cosmology and go on to analyse the deviations
from the LCDM predictions in the linear regime. We find that for reasonable
values in the model's parameter space there is generically a region where the
model's cosmology is viable and current measurements can be reproduced. A small
discrepancy of the matter power spectrum from its LCDM counterpart can be
obtained in a smaller subset of the parameter space.
