Special equipment: Six 12-inch metal skewers or twelve 6-inch bamboo skewers
Prepare an outdoor grill or a grill pan for medium heat.
Whisk together 1 tablespoon of the oil and the lemon zest in a large bowl. Add the chicken to the oil and toss to coat. Sprinkle with salt and pepper. Divide the chicken and thread onto metal or bamboo skewers.
Toast the pine nuts in a small skillet over medium heat, tossing frequently, until light golden, 3 to 4 minutes. Let cool.
Combine the pine nuts, basil, parsley, garlic, 1/2 teaspoon salt and several grinds of pepper in a food processor. Process to make a coarse paste. Add the avocado, lemon juice and remaining 3 tablespoons oil and process until mostly smooth.
Grill the chicken, turning often, until just cooked through, 5 to 7 minutes. Serve the chicken dolloped with the pesto and any extra pesto on the side.
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