The origin is somewhat surprising. It dates back to Old English, according to the OED's entry for it:
As the subject of an existential clause: = there adv. 4d. Now chiefly U.S. regional (south. and south Midland).
In Old English esp. with following that-clause; compare A. 4a(b).
The earliest example they give is this one, from "early Old English" (luckily I was able to find a translation):
Is hit lytel tweo ðæt ðæs wæterscipes welsprynge is on hefonrice; ðæt is Halig Gæst.
Gregory's Pastoral Care by King Alfred
There is little doubt that the well-spring of this wæterscipe is in heaven, that is the Holy Spirit.
A Handbook of Anglo-Saxon Studies
In addition, some examples from Middle English can be found here under 4b.(b).
From circa 1384 (?), written by John Wycliffe, an early translator of the Bible into English and a devout anti-papist reformer:
And ȝif men speken largili, many men ben here more blessid þan þe pope; for hyenes of þis state makiþ not bi himsilf man blessid, for ellis ech pope were blissed, al ȝif he were falsly chosen of fendis; and Scariod shulde be blissed, as he was chosen by Crist himself. And it is no nede to argue here for to disprove þis foli, for it is more fals in himsilf þan ouȝt þat men shulen bringe herof.
These writings appear in The Select English Works of John Wyclif, edited by Thomas Arnold, Volume 3, and published in London in 1871 (pp. 344-345).
[yogh (ȝ) approximates "y" or "ou" (as in ouȝt = ought); thorn (þ) approximates "th"; "hyenes" = highness; "foli" = folly, etc.]