Prepare the wild rice according to the package instructions.
Meanwhile, cut a 1/2-inch slice off the top of each tomato. Scoop out and discard the seeds, most of the flesh and excess juice. Place the tomato shells on a baking sheet and set aside. Preheat the oven to 350 degrees .
In a large skillet, heat 2 tablespoons olive oil over medium heat. Add the onion and cook, stirring occasionally, until softened, about 3 minutes. Add the mushrooms and cook for 1 minute. Add the ground chicken and cook for 6 minutes, breaking up the meat with a wooden spoon until crumbly. Stir in the smoked paprika. Remove the pan from the heat and stir in the cooked wild rice, sour cream and dill. Add salt to taste.
Stuff the rice mixture into the tomatoes. brush the outside of the tomatoes with the remaining 1 tablespoon olive oil and season lightly with salt. Cover loosely with foil and bake until the tomatoes are tender and the filling is hot, about 25 minutes.