In a plastic bag combine the chicken, oyster sauce, soy sauce, vegetable oil, and sugar. Smush around in your hands until well combined and all the chicken is covered. Leave for 15 minutes.
Peanut Sauce
In a saucepan over medium heat add the red curry paste and peanut butter, stirring while cooking. Continually add small parts of the coconut milk mixing each time to ensure that the peanut butter doesn’t remain in globs but rather is a smooth part of the sauce. Continue adding until all the coconut milk is used.
Season the peanut sauce with the sugar and fish sauce, then bring to a slow simmer while starting the steamed vegetables.
Remove the chicken from the marinade. Add the chicken to the simmering sauce, making sure to break up any clumps. Continue to simmer the chicken in the sauce until it is cooked through. Remove from the heat.
Steamed Vegetables
Set up a steamer with the water at a gentle boil.
Add all the vegetables to the steamer and let cook until fork tender.
To Serve
Divide the vegetables between each plate. Top with a portion of the chicken and a generous portion of the peanut sauce. Serve immediately.