Sauté Brussels sprouts in olive oil over medium high heat until the sprouts have browned slightly on all sides (about 8 to 10 minutes). Season lightly with salt and pepper at the start of cooking.
Lower heat to medium and add chestnuts, sauteeing for an additional 4 to 5 minutes.
Add stock, broth or water and cook uncovered until the Brussel sprouts are just tender, about 4 minutes.
Taste and correct the seasoning with salt and pepper, if necessary.