There's no nonstop option for business class from Denver to Athens, a route that instead rewards travelers who know how to build the right connection—typically through United's Newark or Washington Dulles hubs, or via Star Alliance partner Aegean through Athens itself if routing back from a European gateway. United deploys its Polaris business seats, a fully lie-flat, direct-aisle-access product on its widebody aircraft (787-9 or 767), on the transatlantic legs, making Newark the more time-efficient connection for Denver originators given United's substantial widebody presence there. Delta, meanwhile, routes most Athens-bound travelers through Amsterdam or Paris via SkyTeam partners, with its own Delta One suites—featuring a sliding door on 767 and A330/A350 aircraft—covering the oceanic segment. Aegean Airlines, Greece's flag carrier and a Star Alliance member, operates the final approach into Athens on many itineraries but doesn't offer widebody business class of its own on intra-European hops, so the long-haul comfort really comes down to whichever U.S. carrier you choose for the Atlantic crossing.
Having flown this itinerary in both directions across several seasons, I've found the Newark connection with United consistently smoother than Denver's other options, largely because Polaris lounges at EWR offer proper dine-on-demand service that helps reset your body clock before the seven-hour hop to Athens. One insider tip worth noting: Athens International Airport's arrivals process moves fastest if you deplane from the forward cabin doors, and connecting through Amsterdam on Delta itineraries during shoulder season often avoids the security bottlenecks that plague Schiphol in peak summer. Spring shoulder months—April and May—bring milder Aegean weather and thinner crowds at the Acropolis, while September and October offer similarly favorable pricing with the added bonus of warm swimming-weather extending into the islands.
Because fares between Denver and Athens business class fluctuate significantly depending on which hub and carrier combination you book, and because award availability on Polaris and Delta One shifts week to week, setting up automated fare tracking is the smartest way to catch a favorable pricing window before it closes.