Heat the oil in a large saucepan over medium heat. Once the oil is glistening, add the curry paste, garlic, ginger, and lemongrass. Cook, stirring constantly, until fragrant, about 2 minutes.
Stir in the chicken stock, coconut milk, sugar, fish sauce, lime juice, and salt. Bring to a simmer, then add the butternut squash. Cook until almost tender, about 8 minutes.
Add the chicken, bell pepper, green beans, and basil. Return to a simmer and cook, stirring occasionally, until vegetables are tender and chicken is cooked through, about 8 minutes more.
Serve the curry over the rice and garnish with basil and chiles, if desired.
