Answer 1
The Jewish answer is Yes; though I imagine there are others who would answer differently.
Answer 2
The assumption implicit in the question is that the term "God's Chosen People" is a clearly defined term. Israel is definitely a state created by and for the Jewish People; this is not in dispute. Whether the Jews are "God's Chosen People" is debatable. As Answer 1 notes, it is the Jewish perspective, as well as the perspective of the majority of Christians, that Jews are God's Chosen People. Other Christians hold that the rejection of Jesus made God relinquish his "chosen-ness" from the Jews and placed it on the Christians. Most Muslims believe that due to Jews' and Christians' failure to believe in Mohammed's prophecy, that the God relinquished his "chosen-ness" from them and gave it to the Muslims.
Of course, in many other religions, such as Hinduism, Buddhism, Shenism, African Folk Religions, etc. there is no concept of a "God's Chosen People". Atheism argues that there is no reason to believe that any god/God would chose people.
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Alternative Proposed Answer, for Discussion:
No. It was created BY them.
Israel State Cup was created in 1928.
The state of Israel was founded in 1948.
Modern day Israel is a nation-state with a Jewish majority. There are also numerous Jews elsewhere. The Jewish tradition holds that Jews are God's chosen people, chosen to bear the burden of the Torah, but the Jewish tradition also includes many stories of Jewish governments that failed to live up to their responsibility.
1948
Illegal immigrants.
The Jewish people used to be called Israel, until the political state was established. You can call them the chosen people, or simply 'Jews', in the same way that you would call Mormons 'Mormons'.
Israel was never owned by Europeans, the state of Israel was officially created after world war two. The Hebrew people (Jewish folks) were basically nomadic before then.
The 20th century, specifically May 14, 1948.
The Jewish State of Israel.
Israel.
Israel declared independence and the Arab Nations declared war on it.
At this time there was no state called 'Israel', but it refered to the people. The Holocaust changed the world view in that there was more sympathy for there to be a state for the people of Israel.