God's chosen (i.e. elect) are all those who meet His conditions of repentance and faith in Christ. The Bible never speaks about God choosing individuals before the foundation of the world to heaven or hell. What God chose before the foundation of the world was His gracious and appropriate plan to send His Son to redeem sinners to Himself and restore them to His image. All who meet the conditions to partake in this plan are chosen (i.e. elect) due to their faithful identification with THE Chosen One, Jesus Christ.
1 Peter 2:4-11 "4 To whom coming, as unto a living stone, disallowed indeed of men, but
chosen of God, and precious, 5
Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ. 6 Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone,
elect, precious:
and he that believeth on him shall not be confounded. 7
Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner, 8 And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed. 9
But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light;10
Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy. 11 Dearly beloved, I beseech you as strangers and pilgrims, abstain from fleshly lusts, which war against the soul"
John 3:17-20 "17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved. 18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God. 19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil. 20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved."
John 3:35-36 "35 The Father loveth the Son, and hath given all things into his hand. 36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him."
The Jewish Believers of the First Church, were the ones spoken of as being the Chosen, the Elect.
These two terms do not relate to Gentiles at all.
Not so. The Christians Peter wrote to were a mix of Jewish and Gentile Christians. All Christians who are submitted to Christ's Lordship and keep His Word are His chosen and elect. Do the following verses only apply to Jewish believers of the First Church? Of course not.
Mark 13:27 "And then shall he send his angels, and shall gather together his
elect from the four winds, from the uttermost part of the earth to the uttermost part of heaven.
James 2:5 "Hearken, my beloved brethren, Hath not God
chosen the poor of this world rich in faith, and heirs of the kingdom which he hath promised to them that love him?"
Luke 18:7 "And shall not God avenge his own
elect, which cry day and night unto him, though he bear long with them?"
Colossians 3:12 "Put on therefore, as the
elect of God, holy and beloved, bowels of mercies, kindness, humbleness of mind, meekness, longsuffering"
And even if you were to make the insane conclusion that these verses only applied to Jewish believers of the first church (whatever you mean by that), it would still prove that choosing and election do not mean what the Reformed Theologians say it means.