Sri Aurobindo
Letters of Sri Aurobindo
CWSA 27
The Author of the Bhagavad Gita
Sri Krishna is not supposed to have written anything. The Gita is part of the Mahabharata which is attributed to the sage Vyasa, the contemporary of Krishna. But in its present form the Mahabharata seems to be of later origin and many scholars say that the Gita was composed afterwards by someone and put into the Mahabharata.
In any case whoever wrote it was a great Yogi and certainly received his inspiration from Krishna.