In large bowl, combine all ingredients. Set aside 1⁄4 cup of mixture for chicken. Scrape remaining butter into 6″-long log on piece of plastic wrap. Roll up, twisting ends to seal. Refrigerate until solid.
Cook Chicken
Fill an 8-quart pot three-quarters full with warm water. Submerge sous vide machine in pot and heat water to 140°F.
Place chicken breasts into freezer bag. Working one breast at a time, lightly pound thicker end with fist, making each breast an even thickness.
Remove chicken from bag. Rub each breast with 1 tbsp Dill Butter.
Place chicken breasts side by side in freezer bag. Leave bag unsealed.
When water has come to temperature, sink all but top of bag in water to let air escape. Clip unsealed bag to side of pot. Cook for 1 hour.
Make Vinaigrette
In large bowl, whisk all ingredients until smooth. Set aside.
Finish Chicken
Remove chicken from freezer bag and place in pan. Heat oil in cast-iron pan over high heat. Cook chicken for 1 to 2 minutes per side, or until golden. Remove from heat.
Assemble And Serve
Divide little gem quarters between 4 plates. Top with radishes and drizzle with vinaigrette.
Slice warm chicken breasts in half and add to each plate. Top chicken with slice of Dill Butter.
