Place the sweet potatoes and bell peppers in the bottom of a 5-quart or larger slow cooker. Pour the water and lime juice over the top.
In a small bowl, combine the curry, smoked paprika, cumin, chili powder, and salt. Place the chicken thighs on a large plate or cutting board, and sprinkle both sides with about 2/3 of the spice mix. Rub to coat, then set the remaining spices aside.
Heat the olive oil in a large skillet over medium-high. Once the oil is hot and shiny, add the chicken thighs and briefly pan sear on each side, just until brown— about 2 minutes for the first side and 1 minute for the second side.
Place the seared chicken in the slow cooker on top of the vegetables. Sprinkle with the remaining spice mixture. Cover and cook on LOW for 4 to 5 hours or HIGH for 2 to 3 hours, until the chicken is cooked through. It should register 165 degrees F on an instant-read thermometer.
Remove the chicken thighs from the slow cooker and transfer them to a cutting board. Once cool enough to handle, cut the chicken into bite-size pieces or shred it with two forks. Set aside.
Pour the coconut milk and cornstarch slurry into the slow cooker, and stir to combine with the vegetables and cooking liquid. Turn the slow cooker heat to HIGH, cover, and cook for 15 minutes, until the sauce thickens slightly.
Return the chicken to the slow cooker and stir to combine and coat the chicken in the sauce. Recover and cook for 15 additional minutes on HIGH, until the vegetables and chicken are hot and tender. Serve warm over rice or quinoa or with naan, topped with fresh cilantro.
INGREDIENT NOTE: I do not recommend chicken breasts for this recipe, as they tend to dry out in the slow cooker. If you decide to use chicken breasts, watch the cooking time very carefully, as the chicken will cook more quickly and can easily become too dry.
TO STORE: Store leftovers in the refrigerator for up to 5 days.
TO REHEAT: Mix your desired portion of rice and chicken curry (if not already combined). Warm gently in the microwave or stovetop until heated through.
TO FREEZE: DO NOT FREEZE. Coconut milk will separate and become "grainy" in the freezer.