My experience has been that chain link fences are actually pretty secure. The trick is to anchor the bike at the vertical support post, (preferably with a u-lock encircling/straddling the post), the post is difficult to cut and the *fence* prevents lifting the bike up off the post.

Hipster High Lock ; Hipsters (generally late teen/twenty something, not necessarily bike messenger type) cyclists would lift their light weight "single speed"/"fixed gear" (SS/FG) bikes to the TOP of the 8 ft. tall chain link security fencing surrounding outdoor RAVES/concerts so that the handlebar would hook over the top of the fence, straddling a vertical post then u-locking the bike HIGH OFF THE GROUND.
RAZOR WIRE across the top of the fence? EVEN BETTER. They could then enjoy the entertainment without 'HARSHIN' THEY BUZZ', 'stressin' on they shway fixay gettin' ripped'.

Other cyclist seeing this, found that this technique worked extremely well on the 6 ft. and even 4 ft. tall chainlink (also called CYCLONE) fences. As long as the shorter fence had a horizontal 'spreader' bar or at least a thick steel cable running along the top of the fence between the vertical posts.

CAUTION : While the above techniques are well proven. RESIST the temptation to try to *hide* the bike in a particularly overgrown or 'OUT OF THE WAY' section of fence !!!
ALWAYS REMEMBER given time and privacy ANY locking technique/system can be cracked !!!