The Modern Greek for “time travel” is the unimaginative calque Ταξίδι στο χρόνο (“travel in time”). It does indeed use the chronos word; but taxidi is a mediaeval word which now means “travel, journey” (originally, it was “expedition”). Star Trek was originally rendered in Greek as Ταξίδι στα Άστρα “Journey to the Stars”.
For a more classical word for “travel, journey”, I’d pick πορεία (which also has the connotation of expedition), which would make time travel chronoporia.
But Alberto Yagos is right that the –naut stem is the more usual one for exploration, and we don’t have any English words ending in –poria (or –pory). Chrononautica is a little too… Latinate? Indirect? Chrononaucy would be the normal Anglicisation (via French) of chrononautia, though it looks just odd, as we have no other -naucy words; so maybe chrononautia.
EDIT: Achilleas Vortselas is right: -nautia is too close to nausea. Make it chrononautilia.