In a large skillet, place chicken and the 1-1/2 cups water. Bring to boiling; reduce heat. Cover and simmer for 12 to 14 minutes or until chicken is tender and no longer pink. Drain well. Cool chicken. Cut into cubes (you'll have about 2-1/2 cups).
Meanwhile, to cook vegetables, in a medium saucepan, cook potatoes and carrots in boiling salted water for 10 minutes or until vegetables are crisp-tender, adding zucchini and frozen peas the last 3 to 5 minutes of cooking. Drain and cool.
Drain jalapeno peppers, reserving 2 tablespoons juice. Cover and chill jalapeno peppers. In a small bowl, stir juice and mayonnaise together until smooth.
In a large bowl, combine chicken, potatoes, carrots, zucchini, peas, and tomato. Gently fold in mayonnaise mixture. Cover; chill for 1 hour.
To serve, transfer to lettuce-lined salad plates. Top with jalapeno peppers and garnish with radishes and tortilla chips, if you like. Makes 4 servings.