If it has slack at the output shaft on the tcase, most likely it has a worn chain. Is it slack up and down or as you rotate it? If it's up and down it could be as simple as the ujoint on the front dshaft or a bad output shaft bearing.
The first thing to check and the cheapest to fix and replace are the U joints.
The 2004 Chevrolet Suburban has 41.3 in. of front leg room.
The 2011 Chevrolet Suburban has 64.4 in. of front hip room.
The 2008 Chevrolet Suburban has 64.4 in. of front hip room.
The 2012 Chevrolet Suburban has 65.2 in. of front shoulder room.
The 2006 Chevrolet Suburban has 41.3 in. of front leg room.
The 2010 Chevrolet Suburban has 41.3 in. of front leg room.
The 2003 Chevrolet Suburban has 41.3 in. of front leg room.
The 2009 Chevrolet Suburban has 41.1 in. of front head room.
The 2002 Chevrolet Suburban has 41.3 in. of front leg room.
The 2003 Chevrolet Suburban has 61.4 in. of front hip room.
The 2014 Chevrolet Suburban has 65.2 in. of front shoulder room.