Make the teriyaki sauce:
In a small bowl, whisk together the brown sugar, soy sauce, pineapple juice, and MSG (if using). Set aside.
Prepare the chicken:
Cut each chicken breast in half with the grain, then slice into strips against the grain.
Cook the chicken and vegetables:
Heat the sesame oil in a large skillet over high heat. When hot, add the chicken, chard stems, and the white/light green parts of the green onions. Season with a generous pinch of salt and pepper. Cook, stirring occasionally, until the chicken is golden brown and the chard stems are tender, about 7–8 minutes.
Add sauce and thicken:
Pour the teriyaki sauce into the skillet. Lower the heat to medium-low. In the same bowl used for the sauce, mix the cornstarch with 1 tablespoon of water. Stir the slurry into the skillet and cook, stirring constantly, until the sauce thickens.
Finish with chard leaves and green onions:
Add the chard leaves and the dark green tops of the green onions. Cook, stirring often, until the leaves are wilted and tender, about 1–2 minutes. Remove from heat.
Serve:
Spoon the chicken and chard over steamed rice. Garnish with toasted sesame seeds, if desired.