Interestin, I will take a look. BTW, it seems to work with other fonts, so if this is an issue we can safely say it is with the Trajan Pro 3 font more so than anything else.
Hello Brett,
>> Thank you for the efforts but you are looking at the page using the Mac version of Chrome. The fonts have no issues rendering on the Mac. You must use a PC to test this for PC users.
I'm sorry for not going into more detail in my reply: this was meant to demonstrate that the font files are working correctly. Here is the same screenshot from Chrome on Windows 7, for your comparison:

(Again, with the text size increased to show that it is Trajan Pro 3.)
If the font still doesn't load for you, it would be helpful if you would provide a page that uses Trajan Pro 3 by default so that the Typekit team can more easily debug the display issue.
Unrelated to the loading issues, you will likely see rendering artifacts in Trajan Pro 3 at 14px. Typekit serves Trajan Pro 3 with PostScript outlines for smooth rendering at large sizes on Windows, as explained in this blog post:
http://blog.typekit.com/2012/03/21/inscriptional-faces-from-adobe-type/
Although lots of designers use Trajan at smaller sizes, it wasn't designed to be used that way. If you check out the browser samples for Trajan Pro 3, you will see the there are rendering issues in Windows below about 30px: https://typekit.com/fonts/trajan-pro-3#browser-samples
You might try something like Minion instead. See the example (with code) in that same blog post.
Or, if Minion Pro is not to your liking, there similar serifs in the library that are recommended for paragraph use:
https://typekit.com/fonts?classification=serif&contrast=regular&recommended-for=paragraphs&weight=regular&width=regular
These fonts that have been hand-picked by Typekit's staff for their technical and aesthetic excellence, and they render excellently across all browsers and devices, including Windows.
I hope that this helps; let me know if you have any other questions.
-- liz