The trilemma argument goes something like this:
Jesus claimed to be God. Therefore, either Jesus was in fact God, or else he was a liar or a lunatic. But clearly Jesus was neither a liar, nor a lunatic, so he must in fact be God.
C. S. Lewis presented the trilemma argument in a 1943 BBC radio program, and in 1952 he published the argument in his widely read book Mere Christianity. The Christian apologist Josh McDowell promoted this argument further in 1972, in his bestseller Evidence that Demands a Verdict (see Chapter 7 in the revised edition). The argument is still widely used by Christian apologists, and was recently defended by the Christian philosopher Stephen Davis.
According to Wikipedia, this argument goes back at least to the mid 1800s:
The earliest use of this approach was possibly by the Scots preacher “Rabbi” John Duncan (1796-1870), quoted in 1870 as a saying used by him during his preaching career:
“Christ either deceived mankind by conscious fraud, or He was Himself deluded and self-deceived, or He was Divine. There is no getting out of this trilemma. It is inexorable.” 
The trilemma appears, however, to be a bit older than this. I did some searching on Google and found an instance of an apologetic argument that is very similar to the trilemma in a book published by John Leland in 1733, a century before the preaching of John Duncan:
And there is as little Pretence for fuppofing that he [Jesus] had a Defign to impofe upon others, or to put a folem Cheat upon Mankind, as there is for imagining that he himfelf was impof’d on. 
To “impofe upon others” means to deceive others, and what Jesus being “impof’d on” means is clarified on the page prior to the above passage:
… there is not the leaft Shadow of Pretence for fupposing that he was impos’d upon himfelf by the Warmth of his own Imagination, or in other words, that he was a meer Enthufiaft or Vifionary, that took his own Fancies for divine Infpirations. He appears from the Account given us of his facred Life, to have been calm and fedate, not fir’d by an intermperate enthufiaftic Heat; … judicious Thought runs thro’ his admirable Difcourfes, and a calm Prudence reign’d in his Deportment. He declar’d indeed that he was extraordinarily fent of God… 
Note that this apologetic argument is not focused specifically on “Jesus’ claim to be God” so it is slightly different from the trilemma presented by Lewis and by McDowell. However, the focus on Jesus’ claim to be “extraordinarily fent of God” comes close enough to the mark to consider this to be an early form of the trilemma. In any case, the basic logic is the same. Jesus was either telling the truth, was a deceiver, or was himself deceived about what he claimed. He was not a deceiver, nor was he deceived, so he must be telling the truth.
The same sort of logic was used in the very first work of historical apologetics, but it was used to defend the truthfulness of the apostles, especially the truthfulness of their claim that Jesus had performed miracles and had risen from the dead.
to be continued…
1. “Was Jesus Mad, Bad, or God?”, in Stephen T. Davis, Daniel Kendall, Gerald O’Collins, The Incarnation: an interdisciplinary symposium on the Incarnation of the Son of God (Oxford University Press, 2004), p222-3.
2. http://en.wikipedia.org/wiki/Lewis’s_trilemma, viewed 1/15/09.
3. An Answer to a Late Book Intituled, Christianity as Old as the Creation: In Two Parts. By John Leland, p.43. Published by printed by S. Powell, for Abraham Bradley, 1733.
4. Leland, p.42.