Make the sauce by combining the soy sauce, fish sauce, oyster sauce and brown sugar. Whisk until smooth then set aside for now.
Add the vegetable oil to a deep skillet, coating the bottom and heating over medium. When the pan is hot, add the chicken pieces, allowing them to brown slightly then flip. The chicken is in small pieces, which means it can over cook quickly and become tough. Remove from the pan when finished.
Add a splash more oil to the pan and add the garlic and chopped chilies for about 30 seconds. Add in the onion and bell peppers and cook for about 2 more minutes.
Add the jasmine rice to the skillet and break it up with a wooden spoon, allowing it to stir fry for about 3 minutes.
Push the rice to one side of the skillet, leaving about ⅓ free. Crack the eggs and lightly scramble in the free space. Allow the eggs to mostly cook and then mix into the rice.
Place the chicken back into the skillet and gently stir to combine it into the rice. Pour the sauce over the rice and mix it in well.
Remove the skillet from heat and gently fold in the basil, until it wilts, allowing the flavor to absorb.
Serve the rice right away with lime wedges on the side.