Calvin, among his other points includes the point that we are Unconditionally Elected and chosen by God alone and nothing we can do can help or hurt this fact. What is the Biblical basis for this?
Unconditional Election refers to
There are a couple of versus specifically that are associated with this.
and 1 Peter 1:1-2
The idea is that God knew these people beforehand and chose these people to be saved. It's a similar concept to predestination.
The Calvinist argument can be found here
Richard's answer doesn't address the primary issue of Unconditional Election, which is that God's election of people to salvation is based entirely on himself, not on any criteria about the person.
e.g. Many people ask me if God didn't simply elect the people that he knew would accept salvation.
The Doctrine of Total Depravity implies that there is no merit to base any criteria or condition on.
More directly, in Romans 3:27-30 Paul makes it very clear that their can be no boasting in our salvation. If God had any preference for one type of person over another, then we could use our salvation to boast as evidence of that. But since there can be no boasting, then God must not prefer one type of person over another.
Similarly, in Romans 9:15-18, Paul argues that God makes his decision with no dependence on the man or woman, but entirely on himself.