Yes, you can fly First Class to Greece, but it is a high-fidelity requirement to distinguish between "Domestic/European First" and "International Long-Haul First." For travelers flying within Europe, most airlines (like Aegean or Lufthansa) offer a "Business Class" service that functions as the highest tier, often featuring an empty middle seat and upgraded meals, but rarely a true "First Class" bed. For long-haul travelers coming from the US, Asia, or the Middle East, a "True" First Class experience is available on major carriers like Emirates, Qatar Airways, and Singapore Airlines into Athens (ATH). Emirates, for example, frequently operates its Boeing 777 with private First Class suites on the Dubai-Athens route. If you are flying from the US, you will likely fly a "High-Fidelity" Premium Cabin like United Polaris or Delta One, which are marketed as Business Class but offer lie-flat seats and luxury amenities. In 2026, for a "True" First Class experience (suites, caviar, showers), you will typically need to connect through a major Middle Eastern or European hub rather than finding a direct "First Class" flight on a US-based carrier.