Bring a large pot of water to a rolling boil. Add the chicken breasts, reduce the heat to a simmer, and let cook for about 20 minutes, or until the chicken reaches an internal temperature of 165 degrees Fahrenheit. [Exact time will vary, depending on the size of your chicken breasts.] When done, use tongs to remove the chicken to a plate & set aside to cool.
Meanwhile, place the rice and 4 cups of water in a rice cooker or small lidded pot. Cook in the rice cooker or according to package instructions until done. Set aside for later.
Once the chicken is cool enough to handle, use your fingers to shred it into bite sized pieces and set aside.
Next, start the curry. In a large enameled cast iron dutch oven, heat the two tablespoons of canola oil over medium-high heat. Add the curry paste and butternut squash and cook for about 5 minutes, until fragrant. I used 4 tablespoons of the Thai Kitchen curry paste because it was somewhat bland... if you use a spicier brand like Mae Ploy, you'll probably only need 2 tablespoons.
Add the coconut milk, fish sauce, and water to the dutch oven. Bring to a boil, then reduce to a simmer and cover. Let cook for about 15 minutes, or until the squash is tender.
Once the squash is tender, stir in 1 teaspoon salt, 1 teaspoon ground black pepper, and 1 tablespoon soy sauce. Add the chicken and simmer for 5 minutes, until warmed through.
Finally, turn off the heat and stir in the lime juice, basil, and cilantro. Add a scoop of white rice to each serving bowl, and spoon the warm curry over top. Enjoy!