  A weakly coupled scalar field $\Phi$ with a simple exponential potential
$V=M_P^4\exp(-\lambda\Phi/M_P)$ where $M_P$ is the reduced Planck mass, and
$\lambda > 2$, has an attractor solution in a radiation or matter dominated
universe in which it mimics the scaling of the dominant component, contributing
a fixed fraction $\Omega_\phi$ (determined by $\lambda$) to the energy density.
Such fields arise generically in particle physics theories involving
compactified dimensions, with values of $\lambda$ which give a cosmologically
relevant $\Omega_\phi$.
  For natural initial conditions on the scalar field in the early universe the
attractor solution is established long before the epoch of structure formation,
and in contrast to the solutions used in other scalar field cosmologies, it is
one which does not involve an energy scale for the scalar field characteristic
of late times . We study in some detail the evolution of matter and radiation
perturbations in a standard inflation-motivated $\Omega=1$ dark-matter
dominated cosmology with this extra field. Using a full Einstein-Boltzmann
calculation we compare observable quantities with current data. We find that,
for $\Omega_\phi\simeq 0.08-0.12$, these models are consistent with large angle
cosmic microwave background anisotropies as detected by COBE, the linear mass
variance as compiled from galaxy surveys, big bang nucleosynthesis, the
abundance of rich clusters and constraints from the Lyman-$\alpha$ systems at
high redshift. Given the simplicity of the model, its theoretical motivation
and its success in matching observations, we argue that it should be taken on a
par with other currently viable models of structure formation.
