Heat grill. Marinate the chicken with 1/2 of the lemon juice, and a generous sprinkling of salt, pepper, olive oil, and dried oregano for at least 20 minutes.
Slice the onion and zucchini into large slices for grilling. Brush slices and Anaheim pepper with oil.
Grill onion and zucchini until thoroughly cooked (the onion should be translucent). Remove from grill and let cool. Grill the pepper until blistered all over. Remove from the grill and let sit. Peel the skin from the pepper (I often wrap my peppers in a kitchen towel to let them sweat before peeling them).
Grill chicken breasts until done (time will vary depending on thickness). Let rest.
Chop onion, pepper and zucchini into small pieces. Slice chicken. Mix together with cilantro, torn into pieces, remaining juice from lemon, and any juices from the chicken. Adjust salt and pepper.