I guess it's transitive since the object is chair.
"Chair" is the object of the preposition "on". "Sit" is intransitive here. " "Sit" can indeed be transitive in other cases, though.
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"Chair" is the object of the preposition "on". "Sit" is intransitive here. If it were transitive, the sentence would be "He sits a chair." "Sit" can indeed be transitive in other cases, though. You can sit a horse, for instance.