The album question has a reasonably clean answer. The band question does not, and the reason is that bands exist before they release anything, so the evidence is demo tapes, set lists and the memories of people who were in the room.
What follows is the honest field: five bands with a real claim, the case for each, and the answer that survives scrutiny.
Exodus, 1979
Exodus formed in the East Bay in 1979 with Kirk Hammett on guitar, and by 1982 were playing material that is unambiguously thrash to audiences at Ruthie's Inn and the Old Waldorf. Metallica moved four hundred miles north partly because of what was happening in that room.
The claim is strong and the evidence is a problem. Bonded by Blood was recorded in 1984 and not released until 1985 because the label fell apart, so a band who were arguably first on stage came third or fourth on record. There is no more brutal illustration of how much the history depends on distribution rather than on chronology.
Metallica, 1981
Formed in October 1981 out of a classified advertisement in The Recycler, on record by July 1983, and the band who completed the assembly. The case is not that they were earliest but that they were the first to have every element in place and to put it in front of the world.
Slayer, 1981
Formed the same year in Huntington Park, playing Iron Maiden and Judas Priest covers at parties, and on record in December 1983. Their claim is to the extreme wing rather than to the form itself, and by 1984 they had gone somewhere nobody else had been.
Exciter, 1978

Exciter from Ottawa are the candidate most often left out of American accounts, and their 1983 debut is contemporaneous with Kill 'Em All rather than derivative of it. Whether it is thrash or extremely fast heavy metal is a genuine argument, and the honest position is that it sits on the line.
Hellhammer, 1982

Hellhammer in Switzerland were doing something so primitive that it bypassed thrash entirely and went straight to what would later be called death and black metal. They belong in any honest survey of the period and they are not the answer to this question.
| Band | Formed | Playing thrash live | On record | Claim |
|---|---|---|---|---|
| Exciter | 1978 | 1981 | 1983 | Earliest, style disputed |
| Exodus | 1979 | 1982 | 1985 | First on stage, last on vinyl |
| Metallica | 1981 | 1982 | 1983 | First complete, first out |
| Slayer | 1981 | 1982 | 1983 | First to the extreme end |
| Hellhammer | 1982 | 1983 | 1984 | A different genre entirely |
The answer
On stage, Exodus. On record, Metallica. And those two facts together are the whole point.
A genre does not exist because somebody plays something in a hall in Berkeley. It exists when the thing is captured, pressed, distributed and heard by people who were not in the room, and that requires a label, a pressing plant and the post. Exodus had the music and no infrastructure. Metallica had both, partly through luck and partly because a couple in New Jersey mortgaged their house.
If that seems unfair, it is, and the members of Exodus have said so with considerable good humour for four decades. It is also how every genre in the history of recorded music has been credited, and pretending otherwise does not help anybody.
The dating of all this is dealt with in When Did Thrash Metal Start?, and the full account of the period is in this part of the history.
Why the evidence is so bad
Everything before the first records is oral history, and oral history about who played what in a hall in 1981 is exactly as reliable as you would expect forty years later.
There are no recordings of most of the early sets. Flyers survive for some shows and not others. The people who were there were teenagers, several of them are dead, and the ones who are alive have been interviewed so many times that their memories have been reshaped by the retelling. Nobody was documenting any of it, because nobody thought it would matter.
What does survive is the demo tapes, and they settle less than people expect. A demo is undated unless somebody wrote on the sleeve, generations of copies drift, and the same songs were rerecorded repeatedly as line ups changed. The tape trading network that carried this music was superb at distribution and hopeless at archiving.
The bands that were nearly first
Three more names belong in the field and are usually skipped.
Anvil in Toronto were making Metal on Metal in 1982, faster and dirtier than anything else a signed North American band had out, and were cited by half the American bands who came after.
Accept in Solingen recorded a track in 1982 that meets the technical definition, and then went back to writing hard rock. If a band can be first by accident and then decline the credit, they did.
And Venom in Newcastle, who were not playing thrash and without whom none of the others would have felt entitled to try. Every serious answer to this question ends up circling back to them, which is a strange fate for three men who could barely play their instruments.
What being first was actually worth
Very little, is the short answer, and the case of Exodus makes the point better than any argument.
They were there earliest, they taught half the East Bay how to play, they lost a guitarist to the band that got out, and their debut sat on a shelf for a year while the label collapsed. By the time Bonded by Blood reached the shops in 1985, the record it should have been competing with was two years old and the band that made it were on a major label.
Forty years later Exodus are still touring, still making records, and still being described as underrated, which is the polite way of saying they were first and nobody noticed. Gary Holt has talked about it with a good deal more humour than most people could manage. The lesson, if there is one, is that priority is a historical curiosity and distribution is a career.
Sources and notes
Formation dates follow the bands' own published accounts. Live dating for Exodus draws on contemporary Bay Area accounts and on the band's later interviews rather than on documented set lists.