depends, what width? what wheels? what tires? how far are you willing to crank the torsion bars and/or cut the fenders/bumper?
If you have stock wheels a 285/75R16 (33x11) will fit fine with a little torsion bar crank. A set of leveling keys a bit of trimming, and a tolerance for having about the same amount of front suspension movement as a shopping cart will clear 305/70R16's (33x12.50) on stock wheels. Aftermarket wheels with less backspacing will require more lift, ie. torsion bars and body lift, or 4" suspension lift. Or lots of creativity with the sawzall or plasma cutter.
I ran a 285/70/17 (32.8 in) BFG All terrain on stock wheels on my 98 f-150 and had no problem with clearance at all. I am not sure how high a stock z71 sits though, but I don't for see having to tighten up the torsion bars and screw up the alignment.
I would say just turn the bars up a lil to get an extra inch or so.
I know a few people running 285's with no problems when turnin the bars.
Mine were turned up when i got it with the stock 265s on it and it still rides like a caddy!