Three letter domain names are the most popular domain names and are very hard to come by (particularly .COMs). Some TLDs allow 2 letter domains, but it is likely that these were taken even quicker.
This tool will allow you to search for available domain names. You can filter with the pull down menus and jump to different pages by selecting the page number above the results. If you hover over the page number, it will show you a preview of the 3 letter domain names on that page.
You can filter the displayed letters from the top pull down menus. Try 'any letter', 'any number', 'alphanum', 'vowel' or 'consenant'. By selecting the random versions, it will pick a different letter each time, rather than applying them in sequence. For example, Letter will try ABCD etc, but Random Letter will pick just one random letter. This gives you more choices when searching for available domain names