Chop the leeks, carrots, celery and garlic. Keep the leeks, carrots and celery in fairly large pieces. Wash the leeks thoroughly - they can be sandy.
Add olive oil to a pot heated over medium heat. Add the leeks, carrots and celery. Sauté for 3-4 minutes.
Add the garlic and sauté for 3-4 minutes, until softened.
Add the chicken broth and bring to boil.
Add the chicken thighs and let cook for 8-10 minutes, until the internal temperature reads 165°F.
Remove the chicken from the broth and place on a cutting board. Turn the temperature down to medium low. Add the salt and pepper to taste.
Using two forks, shred the chicken, removing any excess fat, and return to the pot.
Let the soup cook at a low simmer (tiny bubbles around the perimeter of the pot) for about 10 minutes.
Add the chopped dill and the juice from the lemon into the pot.
Place ¼ cup or so of the pastina in the bottom of a soup bowl and ladle some of the soup overtop. Cooking the soup and pasta separately will prevent the pasta from becoming soggy.