In the bowl of a blender or food processor, combine all the marinade ingredients: Greek yogurt, parsley, basil, chives, tarragon, garlic cloves, lemon juice, olive oil, anchovy paste, salt, and pepper.

Blend on high until the mixture is completely smooth and creamy, scraping down the sides as needed. The color should be a vibrant green.

Taste and adjust seasoning if necessary. Reserve about 1/2 cup of the marinade in a separate small bowl, cover, and refrigerate. This will be used as a sauce for serving.

Place the chicken breasts between two sheets of plastic wrap and use a meat mallet or rolling pin to pound them to an even thickness of about 3/4-inch. This ensures even cooking.

Place the pounded chicken in a large mixing bowl or a resealable plastic bag. Pour the remaining Green Goddess marinade over the chicken, ensuring each piece is fully coated. Seal the bag or cover the bowl.

Marinate in the refrigerator for at least 30 minutes, or up to 4 hours. Do not marinate for longer than 4 hours, as the acid from the lemon and yogurt can start to break down the chicken texture.

Preheat your grill (gas or charcoal) or an indoor grill pan to medium-high heat (about 400-450°F or 200-230°C). Clean and lightly oil the grates to prevent sticking.

Remove the chicken from the marinade, allowing any excess to drip off. Discard the used marinade.

Place the chicken on the hot grill. Cook for 6-8 minutes per side, or until the chicken is opaque, has beautiful grill marks, and an instant-read thermometer inserted into the thickest part registers 165°F (74°C).

Transfer the grilled chicken to a clean cutting board and let it rest for 5-10 minutes. This allows the juices to redistribute, ensuring a tender, moist result.

Slice the chicken against the grain and serve immediately, drizzled with the reserved Green Goddess sauce. This dish pairs wonderfully with a fresh salad, roasted potatoes, or quinoa.