Cut chicken into 1-in. pieces. Peel and dice sweet potatoes. Chop onion and bell pepper; mince garlic.
Heat the oil in a large Dutch oven over medium-high. Sprinkle chicken with salt and pepper. Cook, turning to brown on all sides, until cooked through; about 5 minutes. Place chicken in a bowl (do not wipe out pan).
Add sweet potatoes, onion, and bell pepper to pan; cook, stirring occasionally, for 3 minutes. Add garlic; cook for another minute. Stir in curry paste and kale; cook until kale wilts, about 2 minutes. Stir in coconut milk and broth and bring to a boil. Reduce heat; cover and cook until potatoes are tender, about 15 minutes. Return chicken to pan and heat through.
Divide quinoa among 4 shallow bowls. Top evenly with chicken mixture and cilantro leaves. Serve with pear slices on the side.