Cook the pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and cherry tomatoes. Cook for 2-3 minutes until the tomatoes start to soften.
Add the cooked chicken back to the skillet, then stir in the pesto sauce and heavy cream. Season with salt and pepper.
Simmer the sauce for 1-2 minutes until heated through and slightly thickened.
Add the cooked penne pasta to the skillet and toss to coat the pasta in the sauce. Cook for an additional 1-2 minutes until the pasta is heated through.
Serve the chicken pesto pasta hot, garnished with fresh basil leaves.