Preheat the oven to 350°F (175°C). Clean and pat dry the chicken breasts.
Arrange the chicken in a 9x13-inch baking dish; drizzle with 2 tablespoons olive oil and the juice of half a lemon. Season both sides with salt and pepper.
Bake the chicken for about 30 minutes, or until no longer pink in the center and the juices run clear. Remove from oven and let rest for 5 minutes.
While the chicken bakes, cook rice according to package instructions and keep warm.
In a medium skillet, melt 4 tablespoons butter over medium heat until it begins to brown slightly.
Add the minced garlic and sauté for about 1 minute until fragrant; do not let it burn.
Add the juice of half a lemon to the skillet and simmer for 1 minute.
Pour in half of the heavy cream, season with salt and pepper, and stir to combine. Simmer for a couple of minutes.
Add the remaining lemon juice and the rest of the cream, stir, and simmer for about 5 minutes, stirring occasionally, until the sauce slightly thickens.
Slice or plate the rested chicken over portions of cooked rice and spoon the creamy lemon sauce over each serving.