Gather the ingredients.
In a medium saucepan, combine the chicken livers, onion, garlic, bay leaf, thyme, and ½ teaspoon of salt. Add the water and bring to a simmer. Cover, reduce the heat to low, and cook, stirring occasionally, until the livers are barely pink inside, about 3 minutes. Remove from the heat and let stand, covered, for 5 minutes.
Discard the bay leaf. Using a slotted spoon, transfer the livers, onion, and garlic to a food processor; process until coarsely pureed.
With the machine on, add the butter, 2 tablespoons at a time, until incorporated.
Add the Cognac, season with salt and pepper, and process until completely smooth.
Scrape the pâté into 2 or 3 large ramekins. Press a piece of plastic wrap directly onto the surface of the pâté and refrigerate until firm.
Serve chilled.
