No, most probably he was not. However, on the web one can find more than one site, mostly devoted to "handicapped" people who nevertheless have become famous due to their impressive achievements, on which Beethoven is given as one of the most striking examples. Most probably the myth about Beethoven being a leftie is the result of the mirrored and often republished print of the Stieler portrait, where the composer has the score of the Missa Solemnis in his left hand and a pencil in the right one. But there's not the slightest trace of a proof that he was left-handed. On the contrary. The only data we have seem to prove that he was right-handed. His handwriting is undoubtedly the handwriting of a right-handed person. Also instructive is the drawing by Klosson. Beethoven is sitting at a table in a public house, holding a newspaper in his left hand and a pipe in his right hand, like all right-handed people. Another proof is a drawing, made in the 1820s, on which we see Beethoven walking, holding a walking-stick in his right hand.