The day before: In food processor, combine butter, garlic, jalapeno, parsley, lemon juice and chives. Season with salt and pepper and process until well-combined. Refrigerate.
On the day: Preheat grill on high. To kill each lobster instantly, place tip of large chef's knife one inch behind the eyes, then blade downward between the eyes in one swift motion. Split lobsters in half lengthwise. Brush meat of lobsters with melted herbed butter, about 1 tablespoon per lobster half. Place lobster on grill, flesh-side down, and cook until meat has grill marks and starts to turn opaque and firm up, about 5 minutes.
Turn lobsters over and grill an additional 5 or 6 minutes, brushing with more butter, if desired. Remove lobsters and place on a large platter. Squeeze lemon wedges all over tail meat, drizzle with olive oil and serve.