The worldwide economic crisis evidently hasn’t affected the rich and famous who annually flock to St. Barts between Christmas and New Year’s.

A view of stunning St. Barts.

The glitzy harbor of this stunningly beautiful Caribbean island was filled with mega-yachts on Sunday, when my cruise ship, the Crystal Serenity, anchored just offshore.

Anchored alongside us was Octopus, the 415-foot-long yacht owned by Microsoft co-founder Paul Allen. The yacht has a swimming pool, a submarine, and fore and aft helicopters. Allen must have been throwing quite a party, because the copters continuously shuttled guests over from nearby St. Martin, which has an international airport.

Happy holidays! Santa Claus arrives at the Palm Court on the Crystal Serenity.

 Each time a helicopter landed, about 10 crew members, looking smart in blue pants and white shirts, scurried to greet the guests. From my stateroom balcony, I trained a pair of binoculars on the yacht, but I didn’t recognize any famous faces.

However, while driving the steep, twisting roads of St. Barts, I entered a roundabout and found myself staring at David Letterman! The CBS talk show host, who has a house on St. Barts, was driving an open vehicle barely larger than a golf cart. Does the CBS insurance department approve of this?

Sporting a couple of days of stubble, Letterman and his wife parked in Gustavia, the bustling capital, and ambled down a street lined with Armani boutiques and Cuban cigar shops. I decided it would be tacky to chase after him and try to get a picture.

My day in St. Barts began early, with a trip to gorgeous Colombier Beach, perhaps the finest on the island. Since it can be reached only by boat or by foot, six of us signed up for a trek arranged by the Serenity’s shore excursion department. Led by Sebastian, a French native who moved to St. Barts 15 years ago, we boarded a van for the short trip to the trailhead. Then we trudged uphill for 45 minutes on the rocky path, which wound through tamarind and mango trees. At times, the path took us to the edge of cliffs with breathtaking views of pounding surf below. Finally, we climbed the last hill and looked down at Colombier Bay.

Trekking the beautiful coves in St. Barts.