(A few hours before serving, or 1 to 2 days ahead) In the bowl of the food process, add the garlic, red pepper, parsley, olive oil, and lemon juice. Pulse several times, until smooth (the garlic and parsley may still be in small chunks). Add the chipotle sauce (optional), sea salt, and black pepper to taste. Pulse a few more times to thoroughly mix. Keep covered in the refrigerator, then allow to come to room temperature before serving. Serve in a small bowl or ramekin.
In the bowl of the food processor, add the garlic, sun-dried tomatoes, pine nuts, basil leaves, and olive oil. Pulse until the mixture forms a paste. Add sea salt and fresh ground black pepper to taste.
Put the cut chicken pieces into the medium bowl. Add the prepared marinade and toss until the chicken pieces are coated and the marinade is evenly distributed. Set aside for at least 1 hour. You can marinade the chicken up to 12 hours ahead of serving, just keep it covered in the refrigerator and allow to come to room temperature before serving.
(Just before serving) In the large sauce pan, bring the stock to a boil, then transfer into the fondue pot. Make sure you do not overfill the pot (some pots have a FILL LINE marked). Add the parsley and garlic and heat according to manufacturers directions.
When the broth is at a simmer, spear a piece of marinated chicken with a fondue fork and put it into the broth. Cook for 2 to 4 minutes depending on the size of the piece. (Chicken should be cooked all the way through before eating.) Dip the cooked chicken into the aioli and enjoy.