I seriously doubt this is true, and even if it were, it would be impossible to determine. What do they mean by "recorded history?" Is it just Europe, or the entire world? What about people whose historical records are lost, or who don't have records for a particular year while other places do?

How do they define "peace" and "war?" War between large states? Uprisings (violent or non-violent) against established regimes? Border disputes between regional chiefdoms? Violent family feuds? Any of these could conceivably be considered a "war."

Although I can certainly imagine a high school course saying something like this, it doesn't seem like the kind of question that a professional historian would ask, and it's definitely not the kind of thing that a professional historian (or any serious writer) would say.

I too have heard that claim and it originates from an article written by Chris Hedges in 2003. No sources are provided and the article has a political message, not a factual one. I'll link it below if anyone wants to read it: http://www.nytimes.com/2003/07/06/books/chapters/0713-1st-hedges.html?pagewanted=1

Hopefully someone will drop by to address that specific claim, but meanwhile, you may be interested in this post from the FAQ

http://www.reddit.com/r/AskHistorians/comments/1j0etg/what_is_the_longest_span_of_time_the_world_has/

Its not a meaningful statement beyond grade school. What would you define as peace? Lack of war? What would you define as war? Formal fighting between states? Would that mean that the Middle East is currently in a state of peace?

Different regions of the world have had their own periods of peace. China has enjoyed fairly peaceful times for hundreds of years multiple times, as has India, the Abbasid Caliphate, Roman empire etc. They dont quite overlap though.

Basically, its a bullshit statement with no context meant to push an agenda. Not saying "world peace" is exactly a bad agenda but it still is one.