- Rinse rice in cold water until water is almost clear. Cook rice according to package directions. Transfer cooked rice to bowl and loosely cover with wet paper towels. Let cool until just warm.
- Place 1 sheet nori on bamboo sushi mat. Wet fingers with water and spread 1 cup rice evenly to cover half of nori, keeping about 1-inch space at the top end of the nori.
- Drizzle 1 Tbsp. black pepper sauce in a line, across the center of the rice. Arrange chicken, avocado, and cucumber on top of sauce in a line.
- Lifting the top end of the mat, carefully roll over the ingredients in the center while pressing and squeezing gently to shape into sushi roll. Repeat with remaining ingredients to make 5 more sushi rolls.
- Wet knife with damp towel and cut sushi rolls crosswise into 1-inch slices.