Preheat your barbecue or indoor grill to high heat.
Cut each avocado in half lengthwise and remove the pit.
Arrange the avocado halves on a baking tray, flesh side up.
In a small bowl, whisk 2 tablespoons of the olive oil with the pinch of salt and pepper and the lemon juice and zest until blended.
Pour this marinade evenly over the avocado flesh, then turn the avocados over to coat the flesh with marinade.
Brush the barbecue with a lightly oiled rag to prevent sticking.
Place the avocados on the grill, flesh side down, for 2 to 3 minutes until charred.
Transfer the avocados to a serving platter, skin side up, and let stand for 5 to 10 minutes to cool slightly.
In a chilled bowl, combine the shrimp, mayonnaise, and chives with the ½ teaspoon of salt until well mixed.
Spoon some of the shrimp mixture into the middle of each barbecued avocado half and drizzle with the remaining 1 tablespoon olive oil. Serve immediately.
