Boil rice in ¾-cup of water in a small pot with a pinch of salt. Cook until rice is tender and keep covered off heat until ready to serve.
Remove and discard any large stems from the kale. Pour a drizzle of oil into a large pan over medium-high heat and add kale with salt and pepper.
Cook for 5-7 minutes, stirring occasionally, and then turn off the heat. Transfer Kale to a plate and add a splash of water to help soften it.
Pat chicken dry with paper towels and season all over with salt and pepper. Heat a drizzle of oil in the same pan over medium-high heat and cook chicken until browned and cooked through (takes about 4-6 minutes).
Reduce heat to medium and add tomato paste, curry powder, and paprika to pan with chicken. Add a pinch of chili flakes if you like things spicy. Let the chicken cook for a minute until you can smell the spices.
Whisk in coconut milk, ¼ cup water, 2 tsp sugar, 1 tbsp butter, and a big pinch of salt. Bring to a simmer, and then reduce heat to low.
Cook for a few more minutes to thicken the curry until thickened, and then add the kale and sour cream. Stir to combine before turning off the heat.
Fluff the rice with a fork and top it with coconut curry chicken to serve.