Brandi Glanville -- My Dog's Been KIDNAPPED

Brandi Glanville claims someone BROKE INTO HER HOME AND STOLE HER DOG ... and now the "Real Housewives" star is on a mission to get her back.

TMZ spoke with Brandi ... she was in Palm Springs with Lisa Vanderpump and Yolanda Foster earlier this week, when she received a call that someone had busted in to her home in Encino, CA and made off with her dog Chica ...her precious chihuahua.

Brandi tells us ... she immediately drove home from Palm Springs and began searching everywhere for her pet.

Brandi says ...when she searched the home, she found a screen on a bathroom window had been ripped open -- the obvious point of entry for the bad guy.

We're told NOTHING else was missing from the home.

Brandi says she filed a report with the LAPD.

Brandi says she's received calls from people claiming to have the dog -- but they've all turned out to be hoaxes.