This paper describes a computational exercise at undergraduate level that demonstrates the employment of Monte Carlo simulation to study the conformational statistics of flexible polymer chains, and to predict solution properties. Three simple chain models, including excluded volume interactions, have been implemented in a public-domain computer program that is the tool on which this exercise is based. The first stage considers fundamental aspects of polymer chain statistics, such as the distribution of end-to-end distance and the exponents in the power laws that relate properties to chain length, for both ideal, phantom chains and also with excluded volume effects. The numerical results are employed to predict properties of real polymer/solvent systems, such as polystyrene in cyclohexane and toluene, which are then compared to experimental data. (Contains 3 figures and 1 table.)