Put the sliced onion, bay leaf, thyme and water or wine in a heavy-bottomed saucepan with a tight-fitting lid. Cover the pan and bring the liquid to a gentle simmer over medium heat.
Set the chicken breast on the onion, then season it with the salt and black pepper.
Replace the lid, reduce the heat to low and cook for 5 minutes.
Take the pan off the heat. Leave it covered for 15 minutes and don’t lift the lid.
Insert an instant-read thermometer sideways into the thickest part of the breast. It must reach 165°F (74°C).
If the chicken hasn’t reached temperature, cover the pan and cook over low heat for another 2 minutes. Check again and repeat if necessary.
Slice or shred the chicken. Use a little of the cooking liquid to moisten it if needed.