Wash and pat dry chicken breasts and season with salt and pepper.
Heat 2 T of the oil in large skillet over medium-high heat until just shimmering.
Cook chicken on one side for 8-10 minutes (depending on how thick breasts are) until golden-brown then flip and continue to cook on other side another 8-10 minutes, scraping together any brown bits. (Add a little extra olive oil if needed and cook a few minutes longer if needed at a medium heat–always check to make sure chicken is cooked thoroughly!)
As the chicken is cooking: In a medium size bowl, combine tomatoes, basil, garlic, vinegar, 3 Tbs oil and about 1/4 tsp salt and pepper (to taste)
Let the chicken cool a few minutes then slice into 2 inch strips (or you can serve the breasts whole, whatever you fancy!)
On a large platter make a bed with the arugula or spinach mixture
Arrange the chicken on top and spoon on the tomato mixture and drizzle the juice over all.