This is going to require some explanation first. I've found that this question is frequently asked but rarely answered to a satisfying degree, with those who ask it often settling for answers like "uh, Chinese, because it's been written down since the 1200's BC" or "well, technically there's no oldest language out there because all languages come from the same source," or some such nonsense. So I'm going to pose it as a scenario.
Let's say you've been given a time machine, and nerd that you are, you've decided to use it to go back in time and find out what a particular ancient culture or civilization was like. The only issue is, you have to be able to speak the language. So which modern language is your best bet for traveling back in time like this, and how far back could you, in theory, go before the language was unintelligible?
So for example, English would be intelligible around 1300 CE but not before, because that's about the time Middle English was becoming Early Modern English. Persian would be intelligible around 800 CE, the time that Old Persian transitioned to Middle Persian. I'm thinking the frontrunners are going to be Greek, Chinese, and maybe Arabic for this, but let's see what people who actually know what they're talking about say.