I don't have a definitive answer, but the following section from Lewis Mumford's 1966 The Myth of the Machine gets at some early charts. Mumford is discussing pre-dynastic Egypt in this section (italics mine):
"If one single invention was necessary to make this larger mechanism [the Megamachine] operative for constructive tasks as well as for coercion, it was probably the invention of writing. This method of translating speech into graphic record not merely made it possible to transmit impulses and messages throughout the system, but to fix accountability when written orders were not carried out. Accountability and the written word both went along historically with the control of large numbers; and it is no accident that the earliest uses of writing were not to convey ideas, religious or otherwise, but to keep temple records of grain, cattle, pottery, fabricated goods, stored and disbursed. This happened early, for a pre-dynastic Narmer mace in the Ashmolean Museum at Oxford records the taking of 120,000 prisoners, 400,000 oxen, and 1,422000 goats. The arithmetical reckoning was an even greater feat than the capture" (192).
The italicized section approaches the original question, though it does not single out the "oldest known chart or graph." I imagine that astrological charts are also some of the oldest, thought I don't have a good source on that. Walter Ong's Orality and Literacy also discusses the earliest uses of writing.
It depends on how you define charts/graphs.
This article* has a pretty good summary of the history of it.
The use of some kinds of visual aid for understanding information is, of course, as old as writing (and probably older). Using standardized graphs to compare numerical quantities in a concise way seems to date to about the 1600s CE, although there are a few scattered examples from a few centuries earlier.
William Playfair (mid/late 1700s) is a name that comes up a lot--from my understanding, he invented the bar graph, [line chart] (https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Playfair_TimeSeries-2.png/800px-Playfair_TimeSeries-2.png), pie chart, and others.
*Friendly, Michael, and Daniel J. Denis. "Milestones in the history of thematic cartography, statistical graphics, and data visualization."
