In a medium bowl, whisk together the lime juice, honey, Tabasco sauce and a pinch of salt and pepper. Add the chicken breast and cover and refrigerate for at least 2 hours, up to overnight.
Once marinated, heat your oven to 350 degrees. Bake the chicken until no longer pink inside, about 25-30 minutes.
Combine all the salsa ingredients in a small bowl and season with a pinch of salt and pepper. Set aside.
In a SMALL food processor (mine is 3 cups) blend together the avocado, garlic, salt, a pinch of pepper and a squeeze of lime juice until smooth and creamy. Add in the basil and use the "chop" setting until broken down. Then, puree until well mixed, stopping to scrape down the sides as necessary.
With the food processor running, stream in the olive oil until well combined.
Place the cucumber noodles into a large bowl and add in the avocado pesto. Toss to evenly coat the noodles (you may need to cut them up!)
Divide the noodles between two plates, followed by the chicken and the blueberry salsa.