Cut the avocados in half, remove the pit, and peel off the skin. Cut the avocados into chunks.
In a food processor, place the basil, parsley, garlic and lemon juice and pulse several times to chop. With the motor on, pour the olive oil in through the top of the machine. Remove the lid, add the avocado and process until the dip is smooth.
Serve the dip in a bowl, garnished with the slivered basil, with the chips arranged attractively around on a platter.