Bring a large, wide pot of salted water to a boil. Add carrots and boil until crisp-tender, about 4 minutes. Transfer to a colander and rinse with cold water.
Add chicken; reduce heat to a simmer. Cook chicken, uncovered, 8 minutes. Remove from heat and let stand, covered, 10 minutes, or until cooked through. Transfer to a cutting board and let cool.
Whisk vinegar, 1 tsp. salt, the oil, pepper, and minced chervil in a large bowl. Cut chicken into thick crosswise slices (against the grain), put in another bowl, and drizzle with half of dressing; turn to coat.
Toss lettuce and carrots with remaining dressing (add any dressing from chicken). Divide among plates; top with chicken, cheese, almonds, and chervil sprigs.
*We are big fans of La Tourangelle brand, found in well-stocked grocery stores and online at latourangelle.com