Preheat the oven to 375°. Season the pork tenderloin with salt and pepper.
In a large skillet heat the olive oil until hot. Add the pork tenderloin and sear all over. When golden color, place in the hot oven.
In a large skillet, melt the butter. Add the chestnuts and cook over moderate heat, stirring occasionally, until lightly browned, about 4 minutes. Add the sliced celery and season with salt and pepper and cook until the celery is crisp-tender, about 2 minutes. Add the stock and cook until the liquid is nearly evaporated and the vegetables are glazed, about 8 minutes.
Remove the pork tenderloin from the oven and slice. Top with chestnut and celery.