Rinse the rice under cold running water until the water runs mostly clear. Bring a medium saucepan of generously salted water to a boil. Add the rice and cook for 5 minutes, until partially cooked but still quite firm in the center. Drain well and spread out on a plate to cool.
Heat 1 tbsp olive oil in a large Dutch oven or deep nonstick skillet over medium heat. Add the leeks and 1/2 teaspoon salt. Cook for 4-6 minutes, stirring occasionally, until soft and reduced in volume but not browned. Transfer to a large bowl and let cool completely.
Add the cooled rice to the leeks along with the ground chicken, dill and remaining 3/4 teaspoon salt, and several grinds of black pepper. Mix until evenly combined.
Form 10 tightly-packed meatballs. If the mixture feels sticky, refrigerate the meatballs for 10–15 minutes before handling.
Heat the remaining 2 tablespoons olive oil in the same pot over medium-high heat until shimmering. Add the meatballs and cook for about 2–3 minutes, turning carefully, until deeply golden brown on one side. They should not be cooked through at this point.
Add the chickpeas and chicken stock. Bring to a boil then reduce the heat to low, cover, and simmer for 12–15 minutes, until the meatballs are firm and no longer pink in the center.
Remove from the heat and squeeze over the lemon juice and garnish with more fresh dill. Taste and add additional lemon, salt, and black pepper as needed. Serve the meatballs and chickpeas in shallow bowls with plenty of the lemony broth and yogurt spooned over top.