In the Bible, there is a story about the Battle of Jericho. This battle, which could not have happened on the dates mentioned in the book if it indeed happened, allegedly resulted in the city's defeat at the hands of the Israelites and the destruction of Jericho's famed 15-foot wall. Even if the battle really took place, it could not have been one of the first battles in history, but what historians and archaeologists have been able to surmise of history's first armed conflicts does involve Jericho.
The settlement of Jericho began about 10,000 BCE, but it took major permanent civilization to allow for the luxury of war. After all, roaming bands of hunters had little worth organizing to fight over and had to keep moving to stay alive. There were likely skirmishes and even some battles during early civilization, but nothing that left evidence for us to find, so far. However, later Jericho appears to have been abandoned at one point during its early history. This, coupled with what appears to be a defensive wall, leads experts to believe that Jericho was attacked.
Remember, any battles that took place in Jericho early could not have been recorded. There was no writing with which to do it. In fact, it is still speculation, given that there are no pictures or weapons left behind to guide us. Weapons would come first.