Preheat a grill to medium. Brush the corn with 1 tsp. EVOO. Grill the corn and bell pepper, turning, until lightly charred on all sides, 15 to 20 minutes; let cool slightly. Meanwhile, brush the zucchini with the remaining 1 tbsp. EVOO; season with salt and pepper. Grill, turning once, until softened, about 10 minutes.
Remove and discard the skin, stem and seeds from the bell pepper and cut the pepper into strips. Slice the corn kernels from the cobs. Cut the zucchini into 1/4-inch half-moons. In a large bowl, combine the peppers, corn, zucchini, edamame, butter and chives; season with salt and pepper. Serve warm.