For the vinaigrette, place all the ingredients in a high-power blender or food processor and turn on. Stream in the oil and combine. Taste and season with salt and pepper; strain and/or transfer to a serving dish and reserve. Note: If you make the vinaigrette in a Ninja or Vitamix blender, it will be smooth enough not to strain. If you use a food processor, you will get a rougher consistency so pass the dressing through a cheesecloth or sieve.
Pre-heat a griddle, grill pan or outdoor grill to medium-high.
Coat the chicken with a drizzle of oil and season with paprika, garlic, onion, thyme, salt and pepper. Grill the chicken for about 7-8 minutes, until cooked thorough. Grill the lemon halves. Douse the chicken with the grilled lemon juice and slice on a the bias into thin strips.
Combine the greens with the onions, chick peas, shaved cheese and almonds and top with the chicken slices and dressing.