[Tolkien indeed overwhelmingly wrote by hand, and for most of his life with a nib/fountain pen. (In fact, the presence of ballpoint pen helps to date his manuscripts; and ballpoint was mostly used for later corrections and additions to earlier manuscripts. ) ...--CFH]
I have read he wrote things like the manuscripts for Lay of Leithian and other manuscripts first in pencil, then filled out in pen.
-- Hans Georg Lundahl
[Yes, Tolkien often wrote in pencil. I didn't mean to imply that he only wrote with a pen. The original question was contrasting typewriter vs. pen composition, and my response was made in that context. --CFH]