In a Dutch oven or a large, heavy pot (at least 5 quarts), heat oil over medium-high. Season chicken with salt and pepper and cook in two batches, tossing occasionally, until browned, about 5 minutes per batch; transfer to a plate.
Add garlic, onion, and oregano to pot; season with salt and pepper. Cook until onion begins to brown, 2 to 4 minutes (don't worry if pan darkens). Add tomatoes (crushing with back of a spoon as you add them) and cook until slightly thickened, 8 to 10 minutes. Add chicken with any accumulated juices and bring to a simmer; cover and cook until chicken is opaque throughout, 2 to 4 minutes.
Add as much escarole to pot as will fit. Cook, tossing and adding more as space becomes available. Cook until escarole is tender, 2 to 4 minutes. Serve stew over couscous.