A weakly coupled scalar field with a simple exponential potential 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 to the energy density determined by the single free parameter in the potential. Such fields arise generically in particle physics theories involving compactified dimensions, with values of the single parameter which give a cosmologically relevant contribution to the energy density. 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 flat dark-matter dominated cosmology with this extra field. Using a full Einstein-Boltzmann calculation we compare observable quantities with current data. We find that with approximately 10 percent of the energy density in the scalar field, 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.