Microwave the lime in a small bowl and set aside until it is just cool enough to handle. In a small bowl, create a slurry by gradually whisking 2 tablespoons water into the cornstarch. Through the feed tube of a running blender add, 1 at a time, the vinegar, chile pepper, garlic, ginger, salt, black pepper, and sugar. Then squeeze the lime from the micro-waved lime through the feed tube into the mixture. Then, leaving the blender running, add the slurry to the sauce, and pour the olive oil in a slow thin stream.
Heat the oil in the deep-fryer to 375 degrees F, or as directed by the manufacturer's instructions for similar foods.
Season the flour with salt and pepper and dredge the chicken strips, allowing any excess flour to fall away. Deep-fry the chicken and drain on paper towels.