To get to another side.
Can we conclude from the indefinite article "an" in "another" that the chicken did not have a definite plan in mind?
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
First things first: as several commentors have pointed out, the standard form of the joke is¹:
Why did the chicken cross the road?
To get to the other side.
That is, the standard joke does use the definite article, which invalidates the premise of the question.
Nevertheless, let us see if we can come up with another example in order to explore the idea that the indefinite article implies lack of certainty.
Let me paraphrase @NicestHippo on Twitter, here:
What should we call this giant advertising board?
PHIL: A philboard
BILL: I have another idea
So from the "a" in another, could you conclude that Bill does not have a definite idea in mind?
No? Not convinced? Alright, let's return to the original joke: just how many sides does a road have, anyway?
¹ See for example, Wikipedia's article on the joke, whose images and references have collected some of its earliest forms and uses, as well as the varieties which have evolved over time: not only is the definite-article version canonical, the indefinite-article version isn't even mentioned or attested.