Since WordPress.com does not support the installation of external themes when on a basic plan, WordPress.com users are unable to install themes via this service unless they are on a WordPress.com Business plan. More information on the difference between WordPress.com, WordPress.com Business and self-hosting can be found here:
If you still would like your purchased theme installed, you will need to either upgrade to a plan that supports third-party themes or purchase separate hosting so that your assigned provider can install the WordPress CMS and your theme. You can see a number of recommended hosts here: http://themeforest.net/get_hosting
Purchasing external hosting will still allow you to keep your chosen URL.