In a medium bowl, whisk together your balsamic vinegar, mustard, and salt and pepper (start seasoning with a pinch each, then after the dressing is done, add more to taste if necessary).
Add about half a tablespoon to the balsamic mixture and whisk again to start the emulsification. Continuing to whisk, slowly drizzle in the rest of the olive oil. Continue to whisk until it all comes together. It should happen rather quickly. Slowly and gradually, drizzle in the oil ensures that the vinaigrette will stay together.
Either toss the greens in the vinaigrette or drizzle the vinaigrette over the greens.
Sprinkle the peach and corn over the greens.
Preheat oven to 375 degrees Fahrenheit. Place a chicken breast onto a baking sheet for the chicken. Drizzle 1 tablespoon of oil (canola, vegetable, or extra virgin olive oil work great) over the chicken breast and toss to cover the chicken with the oil evenly.
Sprinkle a couple of pinches of salt and pepper over the chicken. Roast the chicken for 12 to 20 minutes, depending on the size or thickness of the chicken breast. When done, the chicken will bounce back when poked, and the juices will run clear. Slice and serve atop the salad.