Yes! The easiest way to do this is to register a domain using Shopify. Log in to Shopify, go to PREFERENCES > DOMAINS & DNS in your store admin to register a domain.
Shopify also integrates with an existing web site or a domain name registered with another provider. Ask your domain registrar to point your domain or subdomain to Shopify's servers. For more information click here.
You can access your new store below.