In the two latter periods of the Stone Age, the Mesolithic and the Neolithic, technology improved significantly. Their predecessors, the Paleolithic people, used roughly hewn flints as weaponry and tools, but the Mesolithic saw the wider use of more sophisticated implements, composed of wood, bone, antler and cordage as well as flints. Furthermore, the people of the Neolithic developed polished stone tools, among other things, which were more effective.
So, what is the closest a Neolithic or ideally a Mesolithic person could get to making a sword? I say "what is the closest" because I presume that the main impediment would be how the stone weapons shatter on impact with another blade. Instead, could they perhaps fashion a weapon somewhere between a very long knife and a sword?
Before I post this question, I'd like to ask a few things of you. If there are any errors in my question, or if there's something else impractical about this whole idea, by all means say so in the comments, but without any hate please. If you point it out to me, I'll edit it as soon as I can, and thus the crisis is resolved.
Edit: So, I've gotten a few answers now about real Stone Age sword-like weapons, or clubs embedded with microliths. On that note, I'm going to take the question further and ask - could Stone Age people build a sword that is essentially an elongated flint/bone, with one, thrusting blade?