"For whosoever shall call upon the name of the Lord shall be saved. How then shall they call on Him in whom they have not believed? and how shall they believe in Him of whom they have not heard? and how shall they hear without a preacher? And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the Gospel of peace, and bring glad tidings of good things! But they have not all obeyed the Gospel. For Esaias saith, Lord, who hath believed our report? So then faith cometh by hearing, and hearing by the Word of God" (Rom. 10:13-17).
Notice the order of saving faith - the Gospel is preached; man hears it preached; and whosoever believes and calls upon the name of the Lord, is saved!
Perhaps we are both right, in that the "many are called but few are chosen" (Mt. 22:14). Since the Word says that God does not will that any should perish (2 Pet. 3:9), He, Jesus, and the Holy Spirit, draw all men ("the called") to Jesus (Jn. 14:4; 12:32; 16:7-14). I believe the "elect" very well may be the "the chosen." Examples of those who appear to fall into this category are Jacob (Rom. 9:13), Moses (Ps. 106:23), John (the Baptizer - Lk. 1:11-16), Jesus (Jn. 3:16), the disciples (Jn. 15:16, 19), and Paul (Acts 9:1-20), just to name a few.
Of course, there is another possible explanation that make sense, at least to me. Because God is Omniscient, all knowing, He knew those who would accept His Son, and those who would not, even before the world was formed (Ps. 1:6; Jer. 1:5; Rom. 8:29; 2 Tim. 2:19; 1 Pet. 1:2; etc.). In this view, born again believers would be both called and chosen. Romans 8:29 says, "For whom He did foreknow, He also did predestinate to be conformed to the image of His Son...."
Bottom line: Salvation is the gift of God to all who will believe the Gospel.