"Remember his marvellous works that he hath done, his wonders, and the judgments of his mouth; O ye seed of Israel his servant, ye children of Jacob, his chosen ones." - 1 Chron 16:13 KJV
The lineage of Jacob is a subset of the lineage of Israel. It follows that "chosen ones" is then also a subset of lineage of Jacob in this case. This passage by itself is not stating that all descendants of Jacob are chosen.
Are you saying that the nation of Israel was not chosen?
I'm saying that I see no scriptural evidence that the "nation of Israel" is chosen. There would have certainly been individual people within the nation(s) of Israel that were chosen. The first apostles (except Judas) would have been within that chosen/elect/saved subset.
The nation of Israel was not predestined to be the chosen nation among all the nations?
As a nation? No. Called but not chosen.
Look:
"Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine: And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel." - Exo 19:5-6 KJV
Holy basically means the same thing as elect/chosen, etc. as far as I can tell. You'll notice the
"if" in Exodus 19. If this, then that. We see in the NT that no one but Christ Himself fulfilled the Law and obeyed the covenant perfectly. This tells us that this "if" in Exodus 19 was not fulfilled prior to Christ and therefore Israel never became a Holy Nation by the condition in this passage.
But, there is a Holy Nation described in scripture and that is the nation in Christ.
"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;" - 1 Peter 2:9 KJV
I don't know what you have been reading but the Old Testament proclaims the nation of Israel above all nations.
Israel the nation? Where?
Which nation on earth was Jesus specifically sent to?
Was the tree that Christ cursed "chosen" because He happened by it? Of course not. Chosen/elect has a specific meaning more than just any kind of interaction.
What nationality did Jesus hold?
If a elect person resided in Gomorrah as a citizen of that nation, that person's election or status does not make the whole nation 'elect' or 'chosen'