Kim Kardashian loaded up her baby girl, and took her out in L.A. Thursday to visit the pediatrician. Far as anyone's seen ... this is Chicago West's first public outing, and our first glimpse at her face.

Kim pushed her in a stroller during the visit, and had a nanny and bodyguard in tow. Chicago's coming up on 3 weeks old -- which in Kardashian years ... means she's ready for her own spin-off reality show.