There is for instance Sima Qian, according to Wikipedia the first Chinese historian, who wrote the Shiji (Records of the Grand Historian) in 109 BCE.
But does this primary source still exist, or do historians have only access to copies of it?
More generally: What are the oldest primary sources of recorded history in China, still available?
The Oracle Bones from the Shang Dynasty discovered in 1899 are still revealing plenty of new information and would be considered the earliest primary source of historical information on the Chinese culture. A terrific podcast on Chinese history is called The China History Podcast by Laslo Montgomery http://chinahistorypodcast.com/
I know the question is asking about whether original 2100 year old bamboo versions of Sima Qian's Records of the Grand Historian exist or not. I liked @samuel-russell 's response about source material being tough for just a few decades.
I'd like to note that there are copies of Sima Qian's work available online on the internet in Chinese. And there are also English language versions in books, for example: ISBN 0231081693, ISBN 978-0835106184, ISBN 9780199574391
Another set of old data was a ton of written records as old as 111 BC found on a archeological dig in the 1930s. There are more than 10,000 of them as found. See page xxxvi in this google book. Written on bamboo, wood, and pottery.
The oldest extant Chinese historical inscription that I know of is the Nestorian Stele, which is dated 781 A.D.
The earliest manuscript of the Records of the Grand Historian is allegedly a Song Dynasty (12th century block print), however, many such block prints have fraudulent prefaces because in China older books were more desirable and brought higher prices, so many 16th century block prints were passed off as Song dynasty prints. In many cases the printers executed very elaborate forgeries to make their prints appear to be genuine Song prints.
That being said, there are extant at least some Song dynasty prints which are genuine and have historical content.
Note that you may see references to a 6th century "manuscript" of Records of the Ancient Historian, but my understanding is that this is just bamboo fragments of very dubious provenance. I have not seen these fragments or any archaeological report on them so I don't know how reliable this claim is.
Just as a general rule of thumb the earliest surviving historical inscriptions date from the Tang dynasty. There are some mss that are alleged to be earlier such as some of the Dunhuang manuscripts which are allegedly as early as the 5th century AD, but once again a lot of these claims are spurious or exaggerated. As a rule nearly all the Dunhuang mss are Song dynasty, and I would be suprised if any could be reliably proved to be earlier than 800 AD.
The reason for thinking this is that there are many pre-Tang archaeological sites in China, but they NEVER have inscriptions, except rudimentary ownership marks and things like that. Archaeologists have excavated dozens of pre-Tang tombs, for example, and they never have inscriptions anywhere. For this reason it would seem that writing only developed in China around 800 AD.
** Note on Oral Tradition **
It is important to realize that even in the absence of written documents you can transmit information orally and China had a very extensive oral tradition in which many thousands of students were required to memorize long passages and chronicles. It is based on these memories that later writings were created in some cases.
** Notes on Pre-Tang Historical Original Sources **
As I note above it is difficult to find verifiable documents before about 800 AD, nevertheless various sources, often fragmentary exist, including divinatory inscriptions, inscriptions on bronze vessels, bamboo chits included in burials, and books on silk in some cases. For a summary of the way these sources are used to re-construct history a good book is Before Confucius by Edward Shaughnessy.
