As npetreley has well stated, Calvinist do believe man has a will, but the sinful will of man is not free, but rather bound in sin. This enslavement by mans sin nature, makes man believe he has no need for God. Therefore choice of God is not a option to the sin bound will. Man will think he is not that bad and does not need "saved" from his sins. This "i'm not that bad, I'm a pretty good guy", is just a part of the enslavement found in the sin bound will of man. Another way in which the boundage works, is that sinful man tells himself that he will chose God another day, but will wait to sin more before he chooses God. In this way mans will is seen in action, but his love for sin will always make sin the choice over God. So God really is not a choice at all.
In both cases sin has controled the heart of man into not chosing God. Man loves sin to much to chose God. And/or Man wants to be in control, and not be under Gods rules, but fails to see it is sin that controls him and he is under Gods rule anyway.
So if God left man to his will to chose God, this would be very crude of God for man does not have the power to overcome the power of sin. Yes, they can live a good life and be a good person, but with this comes pride and pride is sin. Man just cannot stop sinning on his own. If God did not step in and break the will of man, man would never believe for sin controls mans will.
Again as npetreley has stated, in regeneration the Holy Spirit, pulls back the blindness and control of sin found in all man, and allows man to see their need for God. This is not forcing man to be saved, but rather it is the Holy Spirit working in the heart of man, to show that they do need God to save them from their sins. When man sees his need for salvation, when he sees Christ as his only hope, when he sees himself as a sinner, when he sees his sins as a problem that he can not address on his own, when he knows that he must wait no longer, he then believes and places all of his faith and hope in Christ to save him from this sin. This pulling back of the sin wall...this unblinding of the blind....this light from God, is the work of the Holy Spirit as man clearly sees for the 1st time his need for salvation. Yes...he is now a believer...for how could he resist? The person must believe, just as the Bible tells us.
I want to point out also....we are saved from SIN, not saved from going to hell. In free-willism, the easy believeism that goes hand in hand with Free-willism, tells the sinner he is saved from hell.