A couple of days ago I received by mail a copy of what seems to be Hugh's first (unpublished) paper (this is  in the quotes below). The title page reads "Discontinuous homomorphisms from C(Ω) and the partially ordered set ω^ω", Hugh Woodin, Fall 1976.
Together with Paul Larson and two other colleagues, I am in the process of editing a volume of proceedings to appear in Contemporary Mathematics, to celebrate Hugh's 60th birthday. There was a meeting in Harvard last year in his honor.https://plus.google.com/+AndresCaicedo0/posts/NmUBxppwoxyhttps://andrescaicedo.wordpress.com/2015/04/01/woodin-meeting/
One of the papers is a lovely survey by Garth Dales on "Norming infinitesimals of large fields". Dales uses the opportunity to recall a couple of anecdotes regarding Hugh.
He says in the introduction: "I first met Hugh in the year 1983-84 when he was one of my TAs for a calculus class that I was teaching at Berkeley. (As a TA, Hugh was initially quite puzzled that there were students at Berkeley who did not understand concepts that were very obvious to him, but he quickly learned about reality.) Subsequently we worked together on two books, and this meant that Hugh came to our house in England quite a few times. This was great pleasure for us. It was something of a shock to my wife and myself to receive an invitation to come to Harvard for a conference to mark Hugh's 60th birthday: how could this charming young man have reached so mature a level?"
He adds some historical remarks at the end: "The paper  was mainly worked out in the year 1973-74, whilst I was at UCLA; I thank Phil. Curtis for inviting me to UCLA and for much support. I gave lectures on this at the inaugural conference on Banach algebras in July, 1974. The work was mostly written in the year 1974-75." He proceeds to explain his result (obtained independently at about the same time by Jean Esterle), namely that, under the continuum hypothesis (CH), given any infinite compact space Ω, there is a discontinuous homomorphism from C(Ω) into some Banach algebra.
He continues: "The paper  was submitted in May, 1976.
"I then thought how one could remove `(CH)' from the theorem, but could not do this; with some trepidation I wrote in June 1976 to Professor Robert Solovay at Berkeley, and asked for his help in this. (Young colleagues might like to know that one wrote by hand on paper in those distant days; but we did have airmail.) This letter eventually reached Solovay at Caltech, where he was on leave.
"The next part of the story is based on information from Frederick Dashiell, then a Bateman Research Instructor at Caltech; I am grateful to Fred for this.
"Hugh Woodin, then a junior at Caltech, approached Fred in January 1976 for a topic for his senior thesis. Fred suggested that Hugh organize what was known about Kaplansky's problem up to that point, and explain the heart of the open question on homomorphisms from C(βℕ). Hugh ignored the survey part of the suggestion, and immediately started trying to construct a model of NDH ["no discontinuous homomorphisms"]; he was learning about forcing at that time, and discussed the question with Solovay, the leading expert on forcing. Hugh produced a type-written document  that I have
in `Fall 1976'; by that time Hugh had seen the preprint of . It seems that this document was not submitted as a senior thesis, and that it has not been published, but results from it are contained in Hugh's thesis  and in . The paper  seems to be Hugh's first contribution to mathematics.
"In fact, Hugh proved in [28,§5] that it is consistent with ZFC that there is an ultrafilter U such that ℓ^∞/U does not admit a non-zero algebra semi-norm, and, in [28,§6], he gave a set-theoretic condition, now `Woodin's condition', which, if satisfied, implies NDH. Subsequently Solovay showed that this condition was consistent with ZFC, and lectured on this on 26 October 1976; this argument was never published because Hugh himself soon gave a shorter proof of the same result. ...
"After some time Solovay kindly replied to my letter, saying that `Woodin' had shown that there are models of set theory in which NDH is true. I wrote to the person that I took to be `Professor Woodin' at Caltech to ask about this, and received  in response."
A short while back there were a post or two here on Woodin's "cryptic marks", https://plus.google.com/+DavidRoberts/posts/TtiW4dMiFcF
Dales also has something to say in this regard: "It will be apparent that the original insights into the theorems of the second half of , including all theorems that involve forcing, were due to Hugh Woodin.
My comment on his method of proof is the following: first, there were discussions on the likelihood that one class was contained in another class, and possible counter-examples were considered; the questions were clarified and the undergrowth cleared away; then Hugh thought about the matter for some time, and drew a large number of squiggly lines on a sheet of white paper; then he opined, using remarkable insight on what would be true in certain models of set theory, that a particular containment would be relatively consistent with ZFC + GCH. These insights were almost always completely correct in the end; but it took many days and many pages to craft a careful proof."
The references mentioned above are
 H. G. Dales, A discontinuous homomorphism from C(X), American J. Math., 101 (1979), 647-734.
 H. G. Dales and W. H. Woodin, An introduction to independence for analysts, London Mathematical Society Lecture Note Series 115, Cambridge University Press, 1987.
 H. G. Dales and W. H. Woodin, Super-real fields: totally ordered fields with additional structure, London Mathematical Society Monographs, Volume 14, Clarendon Press, Oxford, 1996.
 W. H. Woodin, Discontinuous homomorphisms of C(Ω) and set theory, Thesis, University of California, Berkeley, 1984.