I was in Riverwood and i accidentally killed a chicken And it says a bounty has been added. Now Hod and Gerdur are trying to kill me. And every time i try to pay off the bounty with the riverwood Guards, they will yell "IM BETTING ON THE BIG ONE" and "FIGHT". Is this a bug?
You have to pay off your bounty, but sometimes (thanks, Bethesda), the guards attack you without warning.
Here's how you do it.
Run out of the city. Quickly.
Run until you can fast travel to another town (whiterun will do). The Guards should approach you as soon as you enter (Because the Riverwood guards are part of the Whiterun hold) and make you pay up (but without beating the crap out of you).
did you try to sheath your weapon? If you sheath your weapon, the guards should stop trying to attack you and ask if you want to pay, go to jail, etc.
Alternatively, since Bounty (http://www.uesp.net/wiki/Skyrim:Crime) is tracked in the Hold (Province) and Riverwood is part of the Whiterun Hold - as far as I know - you should be able to pay you bounty there to any of the guards.