Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté for 3-4 minutes, stirring occasionally, until softened and translucent. Add the minced garlic and cook for another 1-2 minutes until fragrant. Stir in the chicken base, bay leaf, and dried oregano, then pour in the water. Bring the mixture to a boil—this is when you're creating the flavorful foundation for the entire soup, so don't rush this step.
While the broth comes to a boil, pat the chicken breasts dry and season both sides with sea salt and freshly cracked black pepper. Once the broth is boiling, carefully add the seasoned chicken breasts and the rice. Return to a gentle boil, then reduce heat to medium-low, cover, and simmer for 15-20 minutes until the rice is tender and the chicken is cooked through (internal temperature of 165°F). I find that searing isn't necessary here since the chicken will cook perfectly in the broth and won't dry out—the gentle poaching keeps it incredibly moist.
Remove the pot from heat. Using tongs or a slotted spoon, carefully transfer the cooked chicken to a cutting board and shred it into bite-sized pieces using two forks. Return the shredded chicken to the pot along with the chopped fresh dill. Gently stir to combine and set aside. Carefully ladle 1 cup of the warm broth into a separate bowl and set it aside—this warm broth will be crucial for tempering the eggs in the next step.
In a medium bowl, whisk the room-temperature egg whites until foamy and slightly thickened, about 1-2 minutes. Add the egg yolks and whisk vigorously to combine. While whisking constantly, slowly drizzle in the fresh lemon juice and lemon zest—this creates the classic avgolemono (egg-lemon) mixture that gives this soup its signature creaminess and tang. The constant whisking prevents the eggs from scrambling when heat is applied. I always add the lemon juice slowly while whisking to ensure the eggs emulsify properly and create that silky texture.
While whisking the egg mixture constantly, slowly pour in the reserved warm broth from Step 3 in a thin stream. This gradual tempering prevents the eggs from scrambling and ensures a smooth liaison. Once the broth is fully incorporated, slowly pour the entire egg mixture back into the pot of soup while stirring gently and continuously. The gentle stirring distributes the egg mixture evenly throughout the soup without breaking it up. Do not boil the soup after adding the eggs—the residual heat will cook them through and create that signature creamy texture without any scrambled bits.
Taste the soup and adjust seasoning with additional sea salt and freshly cracked black pepper as needed. Ladle the soup into bowls and garnish each serving with a sprinkle of fresh chopped dill and a drizzle of high-quality extra virgin olive oil. The olive oil adds richness and a peppery finish that's essential to authentic Greek lemon chicken soup.