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Khaire is the imperative form of the same root that gives us kharis (grace, joy, favour) — so a greeting of khaire is, quite literally, a wish that the person (or god) addressed should rejoice. It was used in everyday ancient Greek as we might use "hello" or "greetings" today, but it carried more warmth than a neutral salutation, since it invoked joy directly. The plural form, khaírete (χαίρετε), was used when addressing more than one person or deity at once.
In modern Hellenic practice, khaire (and khairete) is commonly used to open prayers and hymns addressed to the gods — for example, "Khaire, Hekate, Guardian of the Crossroads" — functioning as a respectful, joyful salutation before a petition or offering. Ending a prayer often calls for a different closing formula rather than khaire, since the greeting is properly an opening address.
The word survives today in Modern Greek as a casual "hi"/"bye" (geia, though khaire itself has largely given way to other forms), and its root is recognisable in English derivatives like "Eucharist" (good grace) and "charisma."