What language are the Gathas, the oldest Zoroastrian scriptures, written in?

The Gathas are written in Old Avestan, also called Gathic Avestan.

They are five groups of sacred hymns preserved within the Avesta, the central body of Zoroastrian religious tradition. Their language is an especially archaic form of Avestan and belongs to the Iranian branch of the Indo-European language family. The Gathas are traditionally regarded as the words of Zarathushtra, or Zoroaster, although the precise dates and stages of their composition remain subjects of scholarly discussion.

The seventeen individual hymns contain about 238 stanzas and roughly 6,000 words. They form the oldest linguistic layer of the Zoroastrian canon and are incorporated into the Yasna, the principal liturgical collection. Because the verses are terse, poetic, and grammatically difficult, their interpretation is often uncertain.

Pahlavi and Middle Persian are later Iranian languages used for Zoroastrian translations, commentaries, and religious literature, not the original language of the Gathas. Sanskrit is a related Indo-Iranian language, which can make the comparison tempting, but it is not the language in which these hymns were composed. Old Avestan is therefore the precise answer.