Step 1

Combine anchovies, garlic, herbs, yogurt, and 3 Tbsp. oil in a blender. Finely grate zest from 1 lemon into blender. Cut lemon in half and squeeze juice into blender; purée until smooth. Season dressing with salt and pepper.

Step 2

Pour half of dressing into a large bowl. Using a knife, make 3 short shallow slits across smoother side of chicken thighs (this will help the marinade penetrate quickly); season with salt. Transfer chicken to bowl with dressing and toss to coat with tongs. Let sit at room temperature at least 30 minutes, or cover and chill up to 12 hours. If chilling, let chicken sit at room temperature 1 hour before grilling.

Step 3

Prepare a grill for medium heat; lightly oil grate. Remove chicken from marinade, letting excess drip back into bowl, and grill, turning every minute or so, until cooked through and beginning to char in spots, 8–10 minutes. Transfer chicken to a platter and let rest 5–10 minutes before serving.

Step 4

Cut remaining lemon into wedges. Arrange radishes and more herbs over chicken; drizzle with a little oil and season with salt and pepper. Serve with lemon wedges and remaining dressing.