In what song was the first hardcore breakdown?

I can name the first mXc breakdown.. but you asked for hXc...

well i looked to the first hxc bands.. and their earliest records.. and found:

Bad Brains, Minor Threat, Middle Class, and Black Flag, the fist hardcore bands, never had breakdowns on their early suff.(ie. all of their 1981 albums)

Pantera did. The breakdowns in their songs from albums Cowboys From Hell and Vulgar Display of Power were influential/copis by hardcore acts. Album Cowboys from hell came first, in 1990. Breakdown is from song "Domination"

1981 to 1990? And not even by a hardcore band? Yep.

Breakdowns only stared to be included in the early 90's.

This is Domination from Pantera's legendary preformance at Moscow: http://www.youtube.com/watch?v=ETLAf_9yStU

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And like I pointed out earlier, I do know the first metalcore breakdown. It is Dead Embyonic Cells, by Sepultura, off of the 1991 album Arise.

Breakdown Hardcore

I have been wondering this too. Pantera's This Love is one of the earliest metal songs I listen to with a breakdown.