Toss the sliced chicken with the cornstarch and soy sauce and let it sit while you prep everything else. This quick velvet keeps lean breast meat tender.
Beat the eggs with a pinch of salt. Cut the tomatoes into wedges over a bowl so you keep every drop of juice.
Heat 1 tbsp oil in a wok or wide pan over medium-high. Pour in the eggs and scramble in big folds until just set but still glossy, about 1 minute. They should look slightly underdone. Move them to a plate.
Add another 1 tbsp oil and stir-fry the chicken in one layer until just cooked through, 3 to 4 minutes. Move it to the egg plate.
Add the last 1/2 tbsp oil, then the tomatoes and their juice, the sugar, ketchup if using, and salt. Cook 4 to 5 minutes, pressing gently, until the wedges slump and release a loose sauce.
Return the chicken and eggs, fold everything together for 30 seconds, and turn off the heat. Finish with sesame oil and scallions. Taste for salt; tomatoes vary a lot.