In a bowl, mix together the oyster sauce, soy sauce, and sugar until the sugar dissolves completely. Set aside.
Heat the oil in a skillet or non-stick pan over medium heat, fry half of the basil leaves for about 10 seconds on each side then place on a paper towel.
Add the peppers and garlic to the pan and sauté until the peppers start to soften and the garlic is golden brown.
Add the chicken and brown on all sides. Stir in the lime juice.
Stir in oyster sauce mixture and bring to a low simmer, until the chicken reaches an internal temperature of 160°F using a thermometer. Taste and adjust the seasoning with salt or more lime juice if needed.
Garnish with fried basil leaves, lime wedges, and jalapeno (if using).