The skeleton description says that while it cannot speak it, it can understand the languages it knew in life. Can it not speak because of its undeath or could it learn to speak a language?
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If it was physically capable of speaking, it would be able to speak the languages it knew in life. It still retains its knowledge of them, so *knowing* how to speak a language is not the problem. The problem is that a skeleton lacks lips, a tongue, vocal cords, a voicebox, and lungs. Speaking is simply impossible.

The Monster Manual entry on skeletons says:

> 
> They can't read, speak, emote, or communicate in any way except to nod, shake their heads, or point.
> 
> 
> 

From this, it seems clear that it is meant to be impossible for skeletons to communicate in **any** way other than the given nodding, shaking, and pointing.
By RAW default, no.
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As explained by others it has no basic, default, means of expressing language. It's not about learning the language, it's the capability of the spell/energy powering the skeleton(s). Undeath is not in itself an impediment to speech (see: Liches).

Therefore you need to extrapolate a bit. The RAW description quoted above seems to imply the power source provides bare-minimum world interaction capabilities. And does not extend to advanced capabilities like mimicking a voice (disembodied or otherwise).

But, the "talking skull/skeleton" trope is incredibly common. So...

By customization, yes. (Possibly with the aid of a magic item.)
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It is your game, after all. And creativity is a core value of the gaming experience.

A skeleton is already magically animated, so if you wanted a **specific skeleton** to have the ability to speak, there are several creative ways you could explain the phenomenon.

* A magic item equipped by its creator, or even left over from its previous life. (An enchanted ring or amulet?)
* A slightly more powerful skeleton who gained the ability to speak over time via wild magic or the like.
* A skeleton created with extra riders on the creation spell by its creator. So maybe it was imbued with a secondary spell to allow a disembodied voice.

You could have all skeletons speak of that's how you want to run your world, but that'd be your own custom flavoring.

A speaking skeleton, otherwise, would be **special for some reason**.