Season chicken with salt and pepper, then dredge in flour and shake off any excess.
In a large skillet, heat olive oil over medium high heat. Swirl pan to coat with oil evenly. Brown the chicken (do not overcrowd the pan, and work in 2 batches) for 4-5 minutes on each side or until golden brown and cooked through. 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 but don’t go too far as you don’t want to turn them into sauce. Add garlic, and cook for 30 seconds.
Deglaze the pan with chicken stock or just water or white wine, and with a wooden spoon scrape off any bits stuck to the bottom of the pan. 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.