Pat the chicken breast dry with paper towels and season both sides with half of the sea salt and black pepper.
Heat the extra virgin olive oil in a medium skillet over medium-high heat until shimmering.
Place the chicken in the skillet and sear for 5-6 minutes per side until golden brown and cooked through, then remove to a plate to rest.
In the same skillet, add the diced yellow onion and minced garlic, sautéing for 2 minutes until fragrant and translucent.
Add the dry basmati rice to the skillet, stirring for 1 minute to toast the grains lightly.
Pour in the chicken broth, lemon juice, and lemon zest, scraping the bottom of the pan to release any flavorful browned bits.
Bring the liquid to a boil, then reduce heat to low, cover with a tight-fitting lid, and simmer for 15 minutes.
Remove from heat and let the rice sit covered for 5 minutes before fluffing with a fork.
Stir in the chopped fresh parsley, dill, and the remaining salt and pepper.
Slice the rested chicken breast into strips and serve immediately over the fluffy herb rice pilaf.