Gently simmer chicken in a pot with water for 10 minutes. Strain and set aside to cool. Shred into bite-size pieces.
Set aside 6 big leaves of lettuce as base for the wrap. Place on a serving plate. Shred the rest of the lettuce.
Prepare the dressing by combining garlic, MAGGI Oyster Sauce, calamansi, sesame oil and water. Mix well.
Combine chicken shredded lettuce, onion, jicama, carrot, peanuts and cilantro in a large bowl. Lightly coat with half of the dressing and place on top of every lettuce. Serve immediately with the remaining dressing on the side.