Add onion and chicken to the bottom of a slow cooker. Top with butternut squash.
Mix coconut milk, lime juice, red curry paste, garlic, coconut sugar, ginger paste, and fish sauce. Pour over top of butternut squash.
Set slow cooker on low for 6 1/2 hours.
Once slow cooker is done, remove chicken and pour butternut squash and sauce into a large blender or food processor, leaving a top vent open to release steam. Blend just until smooth, then return to slow cooker.
Shred chicken with two forks and return to slow cooker. Add zucchini, sweet peppers, and Thai basil and return to low heat for 30 minutes.
Serve butternut squash and chicken mixture with rice.