Chris Brown -- Scores Win Over Baby Mama

Chris Brown scored an early victory in his custody war with Nia Guzman that could end up saving him hundreds of thousands of dollars.

There was no sign of Chris during the first part of the hearing in a Houston courtroom ... where the judge shot down Guzman's motion to move the case to California. Although Guzman now lives in Cali ... the judge pointed out she was living in the Houston area when the case was filed.

Brown's attorney opposed the motion to move -- most likely because California courts tend to award more money in child support cases than Texas. Remember, Chris is currently paying Nia $2,500 per month, but she wants to bump that to $15k.

The hearing's still going on -- the judge still has to hash out a custody arrangement, and rule on the gag order Chris wants ... to stop Nia from bad mouthing him.

Even though Chris was NOT initially in the courtroom ... he posted a pic saying he's been in the building all along. We're told he and his attorney Mark Geragos were in a private area.