Make the Lemon Chive Pistou by combing chives, olive oil, garlic, salt, lemon juice and zest. Set aside until ready to serve.
Heat a large heavy bottom pan over medium high heat. Add olive oil and swirl. Pat halibut fillets dry with a paper towel, then season lightly with salt and pepper. Place fillets in middle on pan with space between them.
Sear halibut fillets until they turn opaque half way up the thickness of the fillet. This should take about 3 minutes on a 1 inch thick fillet. Flip over. Add tomatoes, still on the vine, wine, garlic and then butter. Cook for another 3 minutes or until completely opaque.
Remove from pan and plate with tomatoes on the vine. Spoon Lemon Chive Pistou over the top.