Chris Brown Will Be A No-Show at Karrueche Restraining Order Hearing

Chris Brown's lawyers will have a steep mountain to climb Tuesday when they essentially tell a judge, "Who you gonna believe, us or your lying eyes?"

We're told Chris will not appear in the hearing where Karrueche is gunning for a permanent restraining order against Brown, whom she claims has threatened to shoot and kill her, in addition to brutalizing her on several occasions.

Karrueche got a TRO, which is about to expire, and she was required to serve Chris with the petition for a permanent order ... something he dodged until a process server handed him the papers earlier this month as he was leaving his birthday party in Houston.

Big problem for Chris ... the service is on video, and the judge will see it in the courtroom.

We're also told Karrueche will not appear in person ... she'll testify on the phone, because she's shooting a TV show in New Orleans.