Preheat the oven to 350 degrees and lightly grease an 8 x 4 inch glass loaf pan. Cut the carrots into strips the length of the carrots but only 1/4 wide (should be evenly cut 1/4inch square). Parboil for 6 to 7 minutes or until cooked through but still with some texture to them. Puree ground chicken a little bit at a time in a food processor with the oil and vinegar and 1 1/2 teaspoons salt and 1/4 teaspoon pepper. Add cooked shallots, garlic, bread crumbs and egg and puree until very smooth.
Divide chicken puree into 3 bowls. In one add the carrots; in the other the green beans and leave the puree plain in the third. Using your hands mix the vegetables into the chicken mixture in each bowl making sure they are completely coated. Set a tiny bit of plain chicken puree in bottom of loaf pan, spreading it with a rubber spatula to cover entire bottom surface. Then cover with a layer of carrot, keeping carrots in as straight a line as possible. Next layer green bean mixture over carrots. With a spatula layer some plain chicken binder on top of green beans just enough to barely coat them. Then set a row of black olives down the center. Dot olives with a paper thin layer of plain chicken binder. Then repeat green bean layer, then top with the carrot layer and finally a layer of chicken binder which should entirely cover vegetables. Cover the top with buttered brown paper pressing paper directly on top of terrine. Cover top with foil.
Tap the loaf pan on the counter a few times to eliminate air bubbles. Place terrine in a larger pan filled with enough boiling water to reach 3/4 of the way up the sides of the loaf pan. Set in oven and bake for 1 hour.
Remove the pan from the oven. Let terrine rest for another hour or until it is cooler. Leave the foil cover on. Drain off excess water. Run a sharp knife between the terrine and the pan to loosen then carefully turn it upside down on a board. Terrine should come out easily. Pat dry with paper towels. Wrap in plastic wrap, then in foil and let it cool in fridge for 3 hours or overnight.