Don hit it on the head, Death Wobble.
More often than not, it's the front control arm bushings going bad. Look the bushings over for splitting, and rot. If the bushings are bad don't even try to change them, it's a PITA. Just replace the arms, they are only about $10 more for the whole thing, with the bushings already in place.
http://www.quadratec.com/products/56015_004.htm (uppers)
http://www.quadratec.com/products/56015_001.htm (lowers)
You'll need two of each.
While you are checking the bushings, check the balljoints, and tierods.
Solid front axles are VERY sensitive to alignments too.
If the front end is tight, you don't even need the stabiliser. My best friend and I run with a local Jeep club (on designated trails only, TREAD LIGHTLY!). we built a 98 Chero with 8 inches of lift, running 35 x 13.50 tires, no stabiliser, and no death wobble.
