In a 5-quart Dutch oven or heavy pot, heat oil over medium-high. Season chicken with salt and pepper. Working in two batches, cook chicken until browned, 6 to 8 minutes; transfer to a plate (chicken will cook more in step 2).
To pot, add coconut milk, broth, 1/2 cup water, and curry paste; bring to a boil, and stir in rice. Add chicken (with any juices), arranging pieces in a single layer. Cover, and reduce heat to medium-low. Cook, without stirring, until rice is almost tender, 15 minutes.
Scatter bell peppers and green beans on top of chicken mixture; cover, and cook until vegetables are crisp-tender, 8 to 10 minutes. Serve with lemon wedges on the side.
You'll find Thai red curry paste (which keeps indefinitely in the refrigerator) and coconut milk in the Asian-foods aisle. For a spicier dish, stir in a bit more curry paste.