For Pesto: in a mini food processor, combine apricots and rice flour. Pulse until until finely chopped. Remove and set aside. Combine remaining pesto ingredients together until a paste forms (or you get the consistancy you want). Stir in the diced apricots and set aside.

Prepare chicken: either slice horizontally to 'butterfly' the breast (to create a pocket to fill with the pesto), or pound chicken with mallet to 1/4" thick (spread on pesto, then roll-up). Once you have filled the chicken with the pesto, place (seam-side down or use toothpicks to secure so pesto doesn't come out) onto a lined baking sheet.

Bake at 350°F for about 40 minutes. About 10 minutes before removing from oven, spread some apricot preserves (melt in microwave first if too thick to spread) over each chicken breast.