Bring a large saucepan of water to a boil over high heat. Prepare a bowl filled with ice water.
Add the asparagus spear pieces to the boiling water and cook for 1 minute. Add the asparagus tips and cook for 1 additional minute. Drain the asparagus into a sieve and immediately transfer to the bowl of ice water to stop the asparagus from cooking further.
In a medium bowl, stir together the chicken, asparagus and tomato.
Toss with the dressing and basil. Serve over lettuce mix, if desired
In a small bowl, whisk together the vinegar, shallots, mustard, salt and pepper.
While whisking, slowly drizzle in the olive oil. Whisk until combined.