Pat the chicken breast dry with a paper towel to ensure a golden, crispy exterior, then season both sides with sea salt, black pepper, and dried oregano.
Heat 0.5 tbsp of olive oil in a large skillet over medium-high heat; once shimmering, add the chicken and sear for 6-7 minutes per side until cooked through and deeply browned.
While the chicken cooks, trim the ends of the green beans and finely mince the garlic clove.
Remove the chicken from the skillet and set aside to rest on a cutting board.
In the same pan, add the remaining 0.5 tbsp of olive oil and the green beans, sautéing for 4-5 minutes until they are bright green and tender-crisp.
Add the minced garlic to the green beans and sauté for another 60 seconds until fragrant.
Deglaze the pan by stirring in the lemon juice and lemon zest, scraping up any flavorful browned bits from the bottom of the skillet.
Slice the chicken against the grain and serve it alongside the garlic-infused green beans, drizzling any remaining pan juices over the top.