Chloe Grace Moretz Gets Permanent Restraining Order Against Obsessed Fan

Chloe Grace Moretz is now fully protected -- at least legally -- from a man who keeps getting busted by cops for hopping her fence.

Chloe and fam just scored a permanent restraining order, which is supposed to keep the guy away from them for 3 years. The restraining order protects Chloe, her 2 brothers, her sister and her mom. The guy can have no contact -- direct or indirect -- with any of them.

The restraining order replaces the temporary restraining order a judge issued at the beginning of the month.

The guy was arrested outside the actress' Los Angeles home TWICE ... after the guy climbed over their private gate and started banging on windows and doors, trying to gain access to the residence. He got arrested, showed up the very next day, and got busted again.