There's a good deal of confusion in the church as to what exactly the  doctrinal concept of predestination entails.  My own suspicion is that  the current Protestant church deviates rather significantly from  Calvin's own understanding of this doctrine, while the Catholic church  has departed to a comparable extent from its own Thomistic heritage; in  fact, the two are likely very nearly the same.
My own thinking on  this issue has been influenced primarily by Scripture (of course), but  also by the thinking of Calvin and Aquinas.  One way to concisely  present the dilemma (or contradiction, or paradox, or whatever you'd  like to call it) is in the following form:
(1)-Scripture clearly  teaches that God, in some sense, "predestines" those whom He saves,  i.e., He chooses, identifies and singles out those upon whom in His  wisdom He wills to pour out His grace, even "before the foundation of  the universe," and apart from any influence the recipient of salvation  could have had on this choice.  Moreover, the saved cannot even choose  to follow God without His assistance, being "dead" in their sins (to  borrow the language of Ephesians 2); conversely, God's call is  irrevocable and irresistible, which is to say that it is perfectly  effectual.  In other words, a person can become saved if and only if God  has predestined them in the above sense.
(2)-In accordance with  common experience, human beings appear to have a meaningful capacity to  make real choices without external constraint, something which is  commonly referred to in a colloquial fashion as "free will."
(3)-This  so-called free will is incompatible with God's sovereignly predestining  us to be saved, for if God has already chosen us, then how can our  choices be free, i.e., free from external constraint?  How can  injunctions to obey the Lord and be saved be meaningful if we can only  respond to them as a result of God's predestination anyway?
Although  some will complain, I'm doing my best to avoid the technical  philosophical jargon that often tends to cloud the discussion.  The  greatest difficulty I find with this construction of the problem at hand  is the non-Biblical notion of free will.  In particular, I'd like to  look a little more closely at what we mean by "free," or by "without  external constraint."
And this is really the crux of it all.  What one usually thinks of when one speaks of free choice is simply the opposite of  another person attempting to force one's hand; consider, for instance, a power-hungry tyrant who demands that his subjects offer assent to the ideologies of his design, or forces them to obey him in a way which is contrary to their own preferred course of action.  We think of a kind of detestable coercion which violates one's own privilege and responsibility to make conscionable choices on the basis of one's own convictions.
However, proponents of the "free will" hypothesis typically fail to acknowledge the assumptions inherent and implicit in this notion.  In particular, if my actions are truly to be free, i.e., made without a sense of pressure or coercion from anyone or anything other than myself, then I must be the sole origin of the choices to carry out these actions.  Indeed, my own existence must constitute a sufficient explanation for my choices.  In other words, I must be who I am necessarily, and must in fact exist necessarily.
The difficulty is, although Christian theism unhesitatingly recognizes God Himself as possessing such a necessary existence, it leaves no room for such a view of contingent and created humanity.  If I am a contingent being (as of course I am; I could as easily have existed as not), then I cannot function as a sufficient condition for my own choices, and some other explanation is necessary.  As the argument suggests, only God can provide such an explanation.
If I am unable to function as a sufficient condition for my choices, then I also cannot claim to have used "free will" to choose salvation.  Since God alone exists necessarily, He alone acts as a sufficient condition for my choices, as well as those of all other beings with "free will."  It is in at least this sense that God can predestine us to salvation, since there is no longer any ultimate and inviolable sense of human freedom in view.
This construction has a few beneficial qualities.  First, it preserves what we know from Scripture is how God interacts with His human creation.  He is still completely in control, and since all contingent beings derive their existence from Him, the ultimate reason for every event, every subsidiary cause and its effect, and every choice is Him, and Him alone.  Such an understanding, moreover, gives us a healthy glimpse of the majestic transcendence of God.
Best of all, this view does not come to us at the expense of human responsibility.  As some have put it, although God may allow evil for a time to accomplish His greater purposes for His creation, He is never responsible for His creatures' wrongdoing; on the contrary, we ourselves are responsible to exercise the freedom within limitations which He offers to us, and which we are unable to use for anything good until Christ has renovated our hearts.  The thorniest objection I know of to the perspective I am advocating is God's interactions with Pharaoh in the Old Testament.  In particular, who is responsible for this: Pharaoh or God?  The answer appears to be, both, possibly even in the sense given here.  I can't claim to have arrived at a perfectly satisfactory resolution to this , but I feel sufficiently confident in this (I believe to be, Biblical) account of predestination/sovereignty/freedom and its comfortableness with the events detailed in Exodus and revisited in Romans 9, to claim that even these objections present it with no insurmountable difficulties.
