Preheat the oven to 350°F (175°C). Rinse the chicken breasts and pat dry.
Place 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 cooked through and no longer pink in the center. Remove from the oven and let rest for 5 minutes.
While the chicken bakes, cook rice according to package instructions.
Heat a medium skillet over medium heat and melt 4 tablespoons butter until it begins to brown slightly.
Add the minced garlic to the skillet and sauté for about 1 minute until fragrant.
Pour in the juice of the remaining half lemon and simmer for 1 minute, then add half (1/2 cup) of the heavy cream and season with salt and pepper. Stir to combine and simmer a couple of minutes.
Add the remaining lemon juice and the remaining 1/2 cup heavy cream to the skillet, stir, and simmer for about 5 minutes, stirring occasionally, until the sauce slightly thickens.
Slice or plate each chicken breast over a portion of cooked rice and spoon the creamy lemon-garlic sauce over the chicken and rice before serving.