While there is GIMP for advanced image manipulation and then a few other alternatives for more simpler image manipulation or drawing, a new "GNOME Paint" program is in development.
GNOME Paint is a new project that's just begun and is being led by GNOME developer Marcin Kolny. His goal for GNOME Paint is to be a simple drawing application -- think like Microsoft Paint.
It won't be for a long time though that it's likely ready to become part of GNOME core apps but is aiming to be a "GNOME-look-like drawing editor" and still needs to go through a UI/UX overhaul.
More details can be found here