Chains of micrometer-size colloidal particles have been self-assembled that are flexible, mechanically stable, and observable in optical microscopy. The chains sometimes have more than 30 particles, and we call them "polloidal chains". A key aspect of the work is the careful modeling of the interparticle forces between partially flattened polystyrene spheres. This modeling helped us to identify a narrow window of system conditions that produce interparticle physical bonds with a bond energy greater than 15kT, as well as a gap of fluid between particles that enables freely rotating bonds and flexible chains. The formation of the chains is well-modeled using linear condensation growth from classical polymer theory, suggesting that the chains might be used experimentally as large-scale, relatively slow moving models for polymer chains.