Both.
Spellings vary with time and place.
The word comes from the Latin "theatrum". In various languages it
retains a "-tr-" spelling.
British English: theatre
Italian teatro
Spanish teatro
Portuguese theatro
Old French teatre, theatre
modern French théâtre
However:
German, Dutch, Danish: the'ater
Swedish te'ater.
American English now tends to use "theater".
But earlier in the USA:
1798 G. Washington Lett. in Writ. (1893) XIV. 21 The
propriety..of my again appearing on a Public theatre, after
declaring the sentiments I did in my Valedictory Address.
That is G. Washington former Pres. of the USA.
--
Peter Duncanson, UK
(in alt.english.usage)