Make Mustard-Thyme Vinaigrette: In small bowl, whisk together vinegar, mustard, thyme, salt and pepper. While whisking, slowly drizzle in oil until all oil is incorporated.
Divide Mustard-Thyme Vinaigrette equally among 4 pint-sized mason jars. Divide chicken over dressing. Layer remaining ingredients, ending with spinach (you may have to tightly pack spinach into jars). Top with lids and refrigerate up to 4 days. To serve, pour onto plate or bowl, stir and enjoy.