Preheat a grill or grill pan over medium-high. Cook the sausage, turning often, until cooked through, 13 to 15 minutes. Transfer to a cutting board.
In a large bowl, toss the radicchio with 1 tbsp. oil; season with salt and pepper. Grill, turning occasionally, until charred in spots, 5 minutes. Transfer to the cutting board. Slice the sausage and chop the radicchio.
Stretch the dough into a large oval; drizzle with 1 tbsp. oil. Grill until puffed and lightly charred, about 5 minutes per side.
Transfer the grilled dough to a cutting board; spread with the ricotta. Top with the radicchio, sausage and chives; drizzle with the remaining 2 tbsp. oil. Slice into 8 pieces.
