Season the chicken breast pieces evenly with sea salt and black pepper.
Heat the olive oil in a medium saucepan over medium-high heat; add the chicken and sear until golden brown on all sides, then remove and set aside.
In the same pan, add the finely diced yellow onion and minced garlic, sautéing for 2-3 minutes until translucent and fragrant.
Stir in the dry basmati rice, toasting the grains for 1 minute until they smell slightly nutty.
Pour in the chicken bone broth and add the lemon zest, then return the chicken to the pan.
Bring to a boil, then reduce heat to low, cover tightly, and simmer for 15-18 minutes until the liquid is absorbed and the rice is tender.
Remove from heat and let stand covered for 5 minutes; fluff with a fork and stir in the fresh lemon juice, parsley, and dill before serving.