Romans 11:5-6 So too, at the present time there is a remnant chosen by grace. And if by grace, then it is no longer by works; if it were, grace would no longer be grace. (NIV)
I have heard some argue that election is by faith and that is how God makes his choice. Here we see that election is by grace, and grace is given as a gift from God.
Ephesians 2:8 For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God (NIV)