I think I've heard this one before. The word is "had". It takes explaining but I believe this is the correct word which will make the sentence "Had Had had Had Had's had, Had would have had Had Had's had."
ryan-kelly is right, it's 'had'
The sentence I've seen for this is:
John, where James had had 'had', had had 'had had'. 'had had' had had the teacher's approval.
In context, this is about two students writing an essay, one's used 'had' and one's used 'had had'.
Fewer words is: Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo. From Pinker's "The Language Instinct". It means: The buffalo from Buffalo who are butted into by other buffalo from Buffalo in turn buffalo others.