In a liquid measuring cup or small bowl, whisk together the chia seeds and water and let stand for about 20 minutes. (Makes 3/4 cup extra-thick chia gel.)
Prepare an indoor or outdoor grill, or preheat the oven to 475°F.
In a large bowl, use your hands to evenly combine the chia gel, ground chicken, oats, onion, 1/4 cup of the cheese, 2 tablespoons of the olive oil, the parsley, oregano, garlic, 1 teaspoon of the salt, 1/2 teaspoon of the black pepper, and the red pepper flakes. When evenly combined, firmly form mixture into 20 meatballs (about 3 tablespoons each).
Grill over medium heat until well done and brown on all sides, about 15 minutes, rotating only as needed. Alternatively, line a large rimmed baking sheet with aluminum foil and coat with cooking spray. Arrange the meatballs on the baking sheet and roast until well done, about 20 minutes. Insert 4 (10-inch) skewers into cooked meatballs, 5 meatballs each. If necessary, keep warm in 175°F oven while preparing linguine.
Cook the linguine according to package directions. Drain the pasta, reserving 3/4 cup pasta cooking water.
Bring the half-and-half, the remaining 1 tablespoon of oil, and reserved pasta water to a boil over high heat in a large saucepan. Add the drained pasta and toss to combine. Add the lemon juice and toss to combine. Add the remaining 1/3 cup of cheese, 1/2 teaspoon of salt, and 1/2 teaspoon of black pepper and toss to combine.
Transfer the linguine to four large pasta bowls. Top each with a skewer of chicken meatballs, sprinkle with basil and lemon zest, and serve.
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