Heat the white wine in a saucepan or microwave until steam is rising from the top. Pour over the sun-dried tomatoes in a heat-proof bowl and cover with a saucer or plastic wrap. Set aside to rehydrate.
Sprinkle the sliced chicken breasts with salt and pepper. Place a large, heavy-bottomed skillet over medium high heat and add 1 tablespoon of the olive oil. When the oil is shimmery, add as much of the chicken as you can without overcrowding the pan.
Sautee the chicken until just cooked through and lightly browned. Transfer to a plate and repeat with the remaining chicken. Repeat with the remaining chicken, adding 1 tablespoon of olive oil each time. You will probably have 3 batches, depending on the size of the chicken breasts.
When the final batch of chicken has been removed from the pan, add any remaining olive oil and the garlic and stir for about 15 seconds, or until the garlic is fragrant. Add the vinegar stir the remove any tasty bits stuck to the pan. When the vinegar boils up and starts to thicken, add the sun-dried tomatoes in the white wine, the capers, the basil, and return the chicken to the pan. Toss to coat and heat through. Remove the pan from the heat.
Add two cups of mixed salad greens to a plate for each of the desired number of servings and use tongs to arrange about a cup of chicken over each salad. Spoon pan sauces over the chicken, if desired.