Slice chicken into 1/4 inch slices
Pour coconut milk into a zip top bag. Crush peppercorns by placing in separate zip-top bag and whacking with back of a sturdy spoon. Add peppercorns, Tabasco, salt, juice, and garlic to bag. Shake to combine.
Add chicken, press out most of air, and seal bag. Shake to coat and put in fridge to marinate up to 4 hours.
Heat canola oil in a wok or large frying pan. Place a colander over a bowl or medium saucepan. Cut a corner off the plastic bag, and empty contents into strainer. Stir to remove excess marinade, and sautee chicken in hot pan. If chicken is cooked through before marinade has reached boil, remove and keep warm.
Bring marinade to full boil, and boil for at least 3 minutes. (Alternately, you can reserve about 1/3 cup of the marinade before you put chicken into bag.) If you have removed chicken, return it to wok. Add sauce, 2-3 Tbsp at a time to coat chicken. You just want chicken to be coated, not “swimming.”
I used bottled lime juice; juice of one fresh lime would work as well.
Be sure any packaged ingredients (coconut milk, Tabasco sauce, bottled juice, etc) is safe for your allergy set.