Preheat oven to 375 degrees. Toss Brussels sprouts with olive oil, and season with salt and pepper. Roast on a baking sheet for 20 minutes, stirring every few minutes.
While the sprouts roast, in a small sauté pan over medium-high heat, heat a tablespoon of olive oil and cook the onion until just translucent. Add the prosciutto and cook until it is warmed through. Set aside.
When the Brussels sprouts are done, add the chestnuts and continue to roast for another 5 minutes, or until the chestnuts are warmed through.
Combine the roasted Brussels sprouts and chestnuts with the onion mixture in a large bowl, and add the vinegar and herbs. Serve immediately.