Eilish requested that order against 39-year-old Christopher A. Anderson.
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He's accused of showing up at Eilish's childhood home - where her parents still live - five times between late December and early January.
She says the suspect has caused her "substantial anxiety, fear and emotional distress."
Anderson has been ordered to stay away from Eilish, her brother, musician Finneas O'Connell, and two family members.
LAPD takes alleged burglar into custody at Billie Eilish's family home in LA
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Neighbors concerned after break-in at Billie Eilish's family home in LA
Billie Eilish seeking restraining order against man who broke into parents' home in Los Angeles
Billie Eilish seeking restraining order against man who broke into parents' home in Los Angeles