Do we use a comma here? "This, we will do last." vs "This we will do last."

I'm wondering about whether it is correct to use a comma in this situation.

This, we will do last.

vs

This we will do last.

The "this" here is referring to something described in the previous sentence obviously. The comma looks to me a little bit less grammatical and yet agrees better with the vocal pattern where a significant pause is expected.

Which is correct and why? Can they both be correct?

Your sentence is an example of syntax called fronting. Peters in the section on fronting in The Cambridge Dictionary of English Grammar (p135) states:

In conversation, fronting of the clausal object or complement may be achieved simply by promoting it to the start of the clause, as in:

• Raw egg for breakfast I can't stand.
• Wonderful it was indeed!

You'll note that neither the object (raw egg for breakfast) nor the complement (wonderful) is separated from the rest of the sentence by a comma. But as the comments under your question indicate, this is not a matter of grammaticality. The comma is acceptable to emphasise the this and represent a small pause.

Note that there is a related example of fronting (called left-dislocation) where a comma is needed. Namely, when the sentence contains a resumptive pronoun. Peters has the example:

• The last owner, I heard he had moved overseas.

Without the comma the reader or listener is momentarily led down a garden path.