Yes, Shopify does sell domains.  Buying a domain name through Shopify is the simplest way to setup your online store with a professional URL like http://www.yourstore.com.

To buy a domain name for your Shopify store, click Preferences → DNS & Domains.  Type in the domain name you'd like and pick an extension:

Most domains will cost $25 (“.com”, “.net”, “.org”, “.biz” and more). Some domains cost $35 (“.co”, “.me”, “.ws”, “.ch”), and a couple cost $45 (“.tv” and “.mx”). All registration costs associated with the domain name are taken care of.

All domain names bought through Shopify come with the following awesomeness:

• One year of use, automatically renewed until you cancel your domain or Shopify store
• Automatic setup of http://yourstore.com, http://www.yourstore.com, and http://shop.yourstore.com URLs
• Automatic creation of info@yourstore.com and sales@yourstore.com email addresses set to forward to your email address
• Optional integration with Google Apps for more sophisticated email and collaboration requirements
• Optional access to full DNS configuration, in case you need to make manual changes

Read more on the Shopify Domain FAQ.