Place all ingredients, except chopped chicken,* in the bowl of a food processor. Whir until completely mixed with a few larger pieces of tomato remaining.
Transfer to a small bowl and fold in the chicken.
Top with a bit more crumbled feta. Garnish with fresh thyme sprigs (or parsley) if desired.
Serve immediately or cover and refrigerate several hours or overnight. Bring to room temperature before serving.
Notes
*Note: for a whiter colored dip, chop dried tomatoes separately and fold in with the chicken.Storage: Keeps up to a week in the fridge in an airtight container.