Bring a large pot of water to a boil. Add the linguine, cook at a rolling boil until just tender. Drain, rinse under cold water, drain again and set aside in a large mixing bowl.
Place the garlic, vinegar, brown sugar, peanut butter and soy sauce in a food processor. Process for 1 minute. With the motor running, slowly add the sesame and hot chili oils through the feed tube and process until well-blended.
Shred the chicken into 2-inch julienne strips, and then toss with the linguine. Add the sauce plus 4 tbsp of the sesame seeds and toss to coat well.
Cut the asparagus on the diagonal into 1-inch lengths. Blanch in a sauce pan of boiling water for 1 minute. Drain, rinse under cold water and pat dry.
Place the linguine and chicken in a large, flat serving bowl and arrange the asparagus on top. Sprinkle with cucumber and remaining 1 tbsp sesame seeds.
Serve at room temperature.
