Sources close to CB tell TMZ ... the baby capuchin monkey everyone saw his 3-year-old daughter cradling actually belongs to Chris. We're told he bought the exotic pet about 2 months ago ... and her name's Fiji.

As we reported ... Chris got skewered online for appearing to have bought Royalty the monkey ... with scores of fans saying the monkey posed a danger to Royalty, and belongs in the wild.

We're told Fiji's permanent address will be CB's crib, and that's the only place Royalty will get to see her. The monkey's not allowed to go to her mom, Nia Guzman's house. While that might ease safety concern's for Royalty, Fiji still won't be in the wild.

Our sources say Chris really wanted her because his idol Michael Jackson had Bubbles, the chimp. It was pretty obvious he was heading down this path when Chris flipped over one of Mally Mall's pet primates.