Season chicken with salt and pepper, and rub chicken with the basil pesto.
Heat olive oil in a large nonstick skillet.
Add chicken to the skillet and cook for 5 minutes on each side, or until thoroughly cooked.
In the meantime, prepare the sauce by combining flour, garlic, basil pesto, evaporated milk, salt, and pepper in a mixing cup or bowl; whisk until thoroughly combined and set aside.
Remove chicken from skillet.
Return skillet to heat and stir in the tomatoes. If pan is dry, add a little more olive oil.
Cook the tomatoes over medium-high heat for about 1 minute, or until just beginning to soften
Add the prepared sauce to the skillet and bring to a boil.
Place the chicken back in the skillet and cook for 2 to 3 minutes, or until heated through.
Remove from heat.
Garnish with cheese and basil ribbons.
Serve with pasta, rice, and/or salad.