Daniel 1:1, When Was Daniel Written

//According to the Babylonian Chronicles, Nebuchadnezzar reigned from 605-562 BCE, and he began a siege of Jerusalem in 599 BCE (it eventually fell in 597 BCE). About King Jehoiakim, we read this in the Hebrew Chronicles:

Jehoiakim was twenty-five years old when he became king, and he reigned in Jerusalem eleven years. He did evil in the eyes of the LORD his God. Nebuchadnezzar king of Babylon attacked him and bound him with bronze shackles to take him to Babylon. –2 Chronicles 36:5-6

Thus, Jehoiakim reigned from perhaps 608 to 597 BCE. His third year would be 606 BCE. Of course, at that time, Nebuchadnezzar was not yet king, and was several years away from besieging Jerusalem. So, the author of Daniel appears to be in error.

Here’s my question: If Daniel was the last of the Hebrew scriptures written, at about 165 BCE as most Bible scholars surmise, how could he have made so obvious an error? Jehoiakim reigned eleven years, not three. Did he not bother to check his research in the Chronicles?

Or was Daniel written much earlier, before the Chronicles, as some linguists insist?