Can an Unbreakable Vow be made with a Muggle?

Question

Can an Unbreakable Vow be made with a Muggle? Or is is strictly between wizards to make the terms?

Answer 1

Probably

We have no canon example to definitively prove it either way. There's no indication, however, that the participants have to be magical. You do need at least one wand to make the spell work.

“Certainly, Narcissa, I shall make the Unbreakable Vow,” he said quietly. “Perhaps your sister will consent to be our Bonder.”
Bellatrix’s mouth fell open. Snape lowered himself so that he was kneeling opposite Narcissa. Beneath Bellatrix’s astonished gaze, they grasped right hands.
“You will need your wand, Bellatrix,” said Snape coldly.
_{(Half-Blood Prince, Chapter 2, Spinner's End).}

So the Bonder has to be a witch or a wizard, and needs a wand to perform the spell. I see no reason why the other two parties need to be wizards or witches.

Given that magical folk are prohibited from revealing their magic (which would certainly include the Unbreakable Vow) to Muggles by the Statute of Secrecy it's unlikely that this situation would present itself. However, if a wizard wanted to use the spell with a Muggle I see no reason why it would not work.

Answer 2

According to Pottermore, no.

From the Pottermore page on the Unbreakable Vow:

This spell binds a wizard to a promise, who will die if they break it

Type: Spell
Purpose: To bind a fellow wizard to a promise
The effect it has on the recipient: The wizard will die if they break the promise

Thus, not only does the promiser (such as Snape) have to be a wizard, but, as the phrase "fellow wizard" suggests, so does the receiver of the promise (such as Narcissa). And as TheDarkLord points out in his answer, the Bonder (such as Bellatrix) definitely does.

Of course, how seriously we should take the precise wording here is up for debate. Most likely, whoever wrote this Pottermore page didn't take a huge amount of care over the exact details of the wording, and didn't realise they were creating new canon. But technically, it is canon.