How high should a chair rail go on a wall when it is in a living room?

With an 8 foot ceiling... I would place the chair rail so that the top is at a height of 32-37 inches. I went and measured mine when I read your post, and mine are at 32", but I would have liked them best at about 35". That would have course change if you have a ceiling height of more than 9 feet. Hope this helps. Happy decorating!

I agree with the answer above. But, I am curious as to why you would need a chair rail in a living room?

I Install All Our Chair Rail At 36, To Each His Own, Nichols Trim

Chair rails were originally installed at what ever height the chairs were in the room. Over time the rail became more decorative than functional and it appears this is you situation. You can put them at any height you wish but chair rail kits are mostly 36" heights.