Place the chicken breasts in a large plastic storage bag. Seal the bag, leaving a small opening, then use a rolling pin to pound the breasts until they're a uniform thickness. Pour in half the balsamic vinaigrette, then seal the bag and marinate in the fridge for 1 hour.
After the chicken has marinated, grill it until it's done in the middle, about 5 minutes per side. Remove from the heat and set aside to cool slightly. Dice up the chicken when it's cool enough to handle.
Add the salad greens to a large bowl. Add half of the remaining dressing and toss it to coat the greens. Add more if it needs it. Add the strawberries, chicken, green onions, and pecans. Toss it gently a few times until it's all combined. Top with crumbled goat cheese and toss a couple of times.
Place an equal amount of salad down the middle of each tortilla. Roll up, then slice in half.
Serve wraps with chips and extra strawberries