Why did Krishna choose a battlefield as the setting for speaking the Bhagavad Gita?
Whenever Krishna does something, He accomplishes many purposes simultaneously. Krishna chose to speak the Bhagavad-gita to His devotee and friend Arjuna on the Battlefield of Kurukshetra for a number of reasons. Krishna's purpose in coming to the material world is to deliver His devotees from the anxieties of material existence, annihilate those who disturb the universal order, and to reestablish principles of religion. His choice of Kurukshetra for speaking the Bhagavad-gita accomplished all three of these.
Just prior to the war, Arjuna was overcome with resistance; he didn't want to fight. Even though fighting was his nature as a warrior, and the war he was about to fight in was a clear case of righteousness versus unrighteousness, he was so distressed about the consequences of the impending conflict that he lay down his bow.
In the course of speaking the Bhagavad-gita, Krishna reminds Arjuna of the eternality of the soul, the relationship between the infinite Supreme Soul and the individual soul, and how to perfect that relationship through practice of bhakti-yoga, Krishna consciousness. By hearing from Krishna, Arjuna's anxiety is removed, and he becomes divinely inspired to fight for Krishna's cause without hesitation. As a result, he becomes Krishna's instrument for ridding the world of a huge overabundance of ungodly military forces. Everyone who hears their conversation gets spiritual benefit.
Krishna's choice of Kurukshetra as the setting for speaking the Bhagavad-gita is also noteworthy for its extremity. The violence and scale of human loss there was tremendous, and it would be hard to conceive of a more intense scene. Arjuna's questions and Krishna's answers on the nature of reality itself could not have taken place at a more grave moment, proving to the rest of us that if it's possible to be perfectly God conscious in the midst of a gigantic battle, it's certainly possible to think of Krishna in less stressful situations.