A mate of mine made a Chai Beer.
No chai taste, but more in its aroma! Very interesting.
I'd agree with buying the ingredients separately. I'm an old chai-sipping hippy from waaaaay back. Have always made my own. I find store-bought chai has too much black tea in it, and often tea can go stale very quickly.
Here's my recipe for Chai (quantities to suit individual taste):
Whole nutmegs
Whole cloves
Cinnamon sticks
Black peppercorns
Whole Cardamon pods
Orange/Mandarin/Lemon/Tangerine Peel
You can boil this up in a pot, and just keep topping up with water and reboiling. You can do this for a bit before the whole spices lose their flavour (depends on intial quantities though). Pour into your favourite mug, and add teabag, milk, honey as you please.
Voila!
Some people like Star Anise in Chai - I personally find it overpowering. Using whole spices is definitely better too...
Life is like a box of chocolates.... sometimes you get a hard one!