Use a 6-quart slow cooker. Pour the coconut milk into the slow cooker and add the Tabasco sauce and tomato paste. Add the curry, coriander, cumin, and grated ginger. Stir to combine.
Add the chicken to the slow cooker and use tongs to flip a few times, coating each piece with the sauce. Add chickpeas and vegetables; no need to stir.
Cover and cook on low for 7-8 hours, or on high for about 4-5 hours. Stir before serving to distribute the sauce. Serve over rice.
Notes
Nutrition facts not calculated with white basmati rice, as this will vary based on amount you use per serving.