Wash rice several times in large bowl with cold water until water is almost clear. Drain rice in strainer for at least 30 minutes.
Meanwhile, make sushi vinegar and chicken teriyaki. For sushi vinegar: combine ingredients in small pitcher. For chicken teriyaki: combine chicken, sauce and garlic in small bowl. Spray heated small frying pan with cooking-spray oil for 1 second. Cook chicken, stirring, until cooked through. Cool.
Place rice and the water in medium saucepan, cover tightly; bring to a boil. Reduce heat; simmer, covered, about 30 minutes or until water is absorbed. Remove from heat; stand, covered, 10 minutes.
Spread rice in a large, non-metallic, flat-bottomed bowl. Using plastic spatula, repeatedly slice through rice at a sharp angle to break up lumps and separate grains, gradually pouring in sushi vinegar at the same time.
Continue to slice and turn the rice mixture with one hand; fan the rice with the other hand about 5 minutes or until it is almost cool. Cover rice with damp cloth to keep it from drying out while making sushi.
Add rice vinegar to medium bowl of cold water. Place one nori sheet, shiny-side down, lengthways across bamboo mat about 1 inch from edge of mat closest to you. Dip fingers of one hand into bowl of vinegared water, shake off excess; pick up a third of the rice, place across center of nori sheet.
Wet fingers again, then, working from left to right, gently rake rice evenly over nori, leaving 1-inch strip on far side of nori uncovered. Build up rice in front of uncovered strip to form a mound to keep filling in place.
Place one-third of the cucumber, sprouts and chicken in a row across center of rice, making sure the filling extends to both ends of the rice.
Starting with edge closest to you, pick up mat using thumb and index fingers of both hands; use remaining fingers to hold filling in place as you roll mat away from you. Roll forward, pressing gently but tightly, wrapping nori around rice and filling. Working quickly, repeat process to make a total of three rolls. Cut each roll into four pieces. Serve with soy sauce, and wasabi, if you like.
