Turkish coffee is a method of preparation, but I have never known it to be made with chicory. Perhaps you meant cardamom?

I've only ever had coffee made with chicory in New Orleans. Somewhat ironically, supposedly we have the French to thank for that - http://www.cafedumonde.com/coffee :-)

... and coffee made with chicory (mix the ground coffee with ground roast chicory and brew normally) has a very interesting flavor... I find roast chicory much closer in taste to coffee than other roast grains used as coffee substitutes—it has a fairly coffee-like bitterness, for example—but it has its own unique flavor as well, with a nice vegetal/grassy sweetness to offset the bitterness.

You can mix it in any proportion that suits you; I like straight roast chicory too...

It's something not everybody likes, but well-worth trying.

[One warning though: I've found that if you let too much chicory go through a coffee-grinder (e.g. if you mix the beans with the chicory before grinding), it can gum up the grinding burrs...]