In a large skillet, heat olive oil over medium high heat. Swirl pan to coat with oil evenly. Brown the chicken for 4-5 minutes on each side. Transfer onto a plate, cover, and set aside.
In the same skillet, melt butter and add the tomatoes. Stir and cook for 2-3 minutes until they start to soften. Add garlic, and cook for 30 seconds.
Adjust the heat to medium low, add heavy cream and pesto, and stir to combine and cook for 1 minute. The sauce will reduce and thicken a little.
Add the chicken back in, and simmer for 1 more minute. Remove from heat, and garnish with some fresh basil leaves if desired.