For the cilantro-jalapeno vinaigrette: Whisk together the cilantro, lime juice, vinegar, cumin, sugar, jalapeno, 1/2 teaspoon salt and a few grinds pepper in a small bowl. Slowly drizzle in the oil, whisking, until the vinaigrette comes together and is well blended. (The vinaigrette makes enough for about 5 salads; refrigerate in an airtight container for up to 5 days.)
For the salad: Soak the onion in a bowl of cold water for 10 minutes, then drain.
Add the drained onion to a large bowl with the mixed greens, chicken, tomatoes and 2 tablespoons of the vinaigrette. Toss together and season with salt and pepper. Cut the avocado into small pieces. Top the salad with the avocado and a squeeze of lime and sprinkle with the tortilla chips.
If you're taking your salad to go, pack the vinaigrette separately and toss together when you're ready to eat.
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