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The first person to call notes by letter names was a monk and music theorist called Boethius. His musical discourse De Institutione Musica was written in the 6th century.
At that time, "A" was the lowest note used in music, or at least church music. The whole of music was divided into various "modes", inherited from the Greeks, and the idea of the modern "scale" did not really exist (although the (present) Ionian mode corresponds to the major scale, modal theory also underwent some revison in the time since Boethius, and the correspondence with the modes described by him could be contested).
A parrallel line of development (as described by keypeg in an earlier post) gave us the sol-fa (do re mi fa sol la ti do) system, which corresponds to the modern scale. The putting of these two lines of theoretical development together resulted in "C" being the bottom note of the all naturals major scale.
Interestingly, the modern standard piano still has "A" as it's lowest note.