In a nonreactive container, combine the chicken with the marinade ingredients. Swish to combine. Marinate about 2 hours at room temperature or 4 hours in the refrigerator.
Heat a gas grill to high or prepare a hot charcoal fire. Grill the chicken until just done, about 5 minutes per side. Set aside until cool and then pull it apart into long shreds.
While the chicken is marinating or cooling, make the dressing by whisking together the lime juice, oil, jalapeño, serrano, roasted poblano, salt, and pepper. Toss with the shredded chicken.
Just before serving, gently toss the chicken with the salad ingredients. Mound the mixture in a lettuce-lined tortilla, if you like, and serve at room temperature or slightly chilled.