Place almonds in non-stick skillet and set over medium heat. Cook the almonds, stirring occasionally, until lightly toasted, about 4 to 5 minutes. Set almonds aside until needed.
Preheat your indoor or outdoor grill to medium-high. Brush chicken with 2 Tbsp. of the oil; season with salt and pepper. Lightly oil the bars of the grill. Grill the chicken 3 to 4 minutes per side, or until cooked through. Set the chicken on a cutting board.
Whisk and combine the vinegar, juice, honey, mustard, tarragon and remaining 3 Tbsp. oil in a salad bowl. Mix in the strawberries; season with salt and pepper.
Cut each chicken breast, widthwise, into 1" slices. Add the lettuce to the salad dressing and toss to combine. Divide lettuce among 4 plates. Set a sliced chicken breast on each plate. Divide and top salad with almonds and cheese and serve.