Place currants in a small bowl; cover with orange liqueur. Let soak until plump, about 1 hour.
Melt 1/4 cup butter in a large skillet over medium heat. Cook and stir onion and garlic in the hot butter until softened, about 1 minute. Add chicken livers; cook and stir until no longer pink in the center, 5 to 8 minutes.
Place remaining 3/4 cup butter, chicken liver mixture, heavy cream, thyme, and allspice in a food processor; blend until smooth. Transfer to a bowl and stir in currants and orange liqueur. Season pate with salt and pepper.
Divide pate among small ramekins. Refrigerate until firm, at least 3 hours.