It's an interesting problem, I would perhaps go for query expression syntax where it can be done like this
int[] array = {1,2,3,3,4,5};
var query = from item in array.Select((val, index) => new { val, index })
join nextItem in array.Select((val, index) => new { val, index })
on item.index equals (nextItem.index + 1)
where item.val == nextItem.val
select item.val;
Which would extract 3 from the array (or list). Of course, what can be done in query expression can obviously be done in lambda.
Edit Joel's solution is much simpler than mine and if you just need it to work on a List or an array, it is perfect. If you need something more flexible to work against any IEnumerable, then you would aim for something like the above (or something obviously better).