Hi,
Yes, this is completely possible.
If you want it under the same username (timchesonisonline), simply log in to WordPress.com, then go here to sign up for another site. You'll have the option to purchase another domain name if you wish.
If you don't want the new site under your timchesonisonline username, log out out of your WordPress.com account, then go to the signup page to get a new account, site, and domain name.