Cover your bamboo sushi mat with plastic wrap. This will help keep the rice from sticking to it.
Cut the cucumber into thin strips that are as long as your nori sheet is wide.
Next, place the nori sheet onto the plastic wrap with the shiny side facing down. Then press around a cup of rice onto the nori sheet in an even layer leaving around an inch (2 cm) of the top of the nori sheet without rice as this will help seal the roll. Tip: Combine a bowl of water and a splash of rice vinegar and use to wet your hands prior to handling the sushi rice. This will prevent the rice from sticking to your hands.
Place a one to two pieces of chicken across the rice on your nori sheet in a row making sure to have an even layer of chicken across the nori sheet so each piece of the sushi will have roughly the same amount of chicken.
Add two to three of the cooked carrot strips to the rice on the nori sheet along with one to two of your cucumber strips, depending on how well everything fits.
Wet the part of the nori sheet that does not contain rice. Starting at the side of the nori sheet with rice, use the bamboo sushi mat to fold your roll until it's completely enclosed. Once the nori is making contact with the rice, pull back the sushi mat so it doesn't get caught in the sushi. Still using the sushi mat as your guide, finish rolling until the roll is completely wrapped. Then wrap the sushi mat around the roll and gently press, tightening the roll together.Keep in mind that rolling sushi is an art that may take some practice so don’t get frustrated if it doesn’t look perfect your first time. It will get easier the more you do it. Using a sharp knife, cut the roll into 8 pieces. I do this by first cutting the roll in half. Then cutting each half in half. Then cutting each fourth in half. Tip: Be sure to clean and wet the edge of your knife before cutting each roll.
Serve with a ramekin of teriyaki sauce and enjoy!