Suddenly there is a clicking sound while the engine is running. I've narrowed it down to something on the Right side on the front of the engine.

A pulley? Doesn't sound like alternator.. Could the belt be too tight? There is literally NO PLAY at all.. it's on TIGHT.. is that normal?

 

Your belt system works with a tensioner, which adjusts the tension for you, so most likely it is not a belt.

Usually, a clicking is the result of an exhaust leak at the point where the header meets the head. This is generally harmless and is fixed by simply tightening the header down to the head. Another, less common, but probable cause of the ticking you hear could be a rocker arm that has come a little loose. Check your pullies to make sure that they do not wobble AT ALL while the engine is running. Basically, they should be so straight that when the engine is running, you shouldnt be able to tell that they are rotating.