Bring a large saucepan of salted water to boil. Add the chicken breasts. Reduce the heat to medium-low, cover, and gently simmer for about 12 minutes, or until chicken is no longer pink in the middle. Transfer the chicken to a plate to cool. Once cool enough to handle, cut the chicken breasts into bite size pieces.

In a large bowl, combine the mayonnaise, lime zest, shallots, red bell pepper, and jalapeno. Fold in the chicken breast pieces into the mixture to coat. Gently stir in the avocado and season to taste with salt and pepper, if needed.

To make the avocado dressing: Place the oil, lime juice, sour cream, and avocado in a blender. Blend until smooth. Thin to a pourable consistency by adding the room temperature water. You may want to add more or less of the water depending on your preference. Season with salt and pepper, to taste.

Place the lettuce mix in a large salad bowl. Add the amount of dressing, to taste, and gently toss. Divide the chopped salad to individual plates and top with a generous portion of the jalapeno chicken mixture.