Cook the spaghetti according to package instructions.
In a large skillet, heat olive oil over medium heat.
Season the chicken breasts with salt and pepper, then add them to the skillet.
Remove the chicken from the skillet and let it rest.
In the same skillet, add minced garlic and cook until fragrant.
Pour in the chicken broth, lemon juice, and zest; let it simmer.
Incorporate sliced butter gradually, stirring until melted and smooth.
Slice the rested chicken and add it back to the skillet.
Toss in the cooked spaghetti, mixing until well combined.
Top with burrata and garnish with fresh herbs.