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Chloe Grace Moretz Obsessed Fan on Her Doorstep ... Cops Nab Him at House

Chloe Grace Moretz and her family are reeling after a total stranger rolled up to her crib, and brazenly knocked on the front door looking for a face-to-face with the actress.

Law enforcement sources tell TMZ ... the man showed up outside Chloe's L.A.-area home a little before midnight Sunday night. He'd apparently driven there, parked outside, hopped her front entrance gate, and walked right up to her door knockin' ... asking if Chloe was home. 

We're told members of Chloe's family told the guy to beat it, and that they were calling the police. Our sources tell us Chloe was not home at the time of the incident. 

Turns out, the alleged visitor didn't go far -- when cops showed up, they found the man sitting inside his car, just chillin', and waiting outside Chloe's house. We're told he was arrested for misdemeanor trespassing.

As of Monday, we're told the man is still in custody on $1,000 bail. 

This isn't the first time Chloe's had to deal with bizarre run-ins -- she got a permanent restraining order against an alleged stalker in late 2017 ... and had to call cops on another guy who tried offering her cookies earlier that same year. 

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