Season the chicken breast with sea salt and black pepper on both sides.
Heat half of the olive oil in a skillet over medium heat and cook the chicken until golden and the internal temperature reaches 165°F.
While the chicken cooks, use a spiralizer to turn the zucchini into thin noodles and pat them dry with a clean towel to remove excess moisture.
In a food processor, combine the fresh basil, walnuts, garlic, lemon juice, nutritional yeast, and the remaining olive oil, pulsing until the mixture is smooth.
Transfer the pesto mixture to a small bowl and fold in the Greek yogurt until the sauce is creamy and uniform.
Remove the chicken from the skillet, let it rest for three minutes, then slice it into thin strips.
Add the zucchini noodles to the same skillet and sauté for 2 to 3 minutes over medium-high heat until just softened but still crisp.
Remove the skillet from the heat, toss the noodles thoroughly with the creamy pesto sauce, and serve immediately topped with the sliced chicken.