The correct option is A Shall
Option A: 'Shall' is a modal that is used to express a suggestion or a polite offer in interrogative sentences. It is also used to know the desire of a person. It relates to the given sentence, as the person is offering to get someone, 'you', a chair.
Hence option A is correct.
Options B and C: 'Have to' and 'had to' are not the correct constructions used in interrogatives, especially when used in the beginning of the sentence.
Hence B and C are incorrect.
Option D: 'Might' expresses permission, e.g. 'might I use your phone?'
It does not express an offer, hence option D is incorrect.