Hi there!
I was reading a Wikipedia page on my hometown in New Jersey, and the history section mentioned (or seemed to imply) that it was the site of the first such killing:
In 1609, Henry Hudson sailed into the Sandy Hook Bay and wrote: "This is very good land to fall in with and a pleasant land to see. Our men went on land, so they went up into the woods and saw great stores of very goodly oaks and some currants". One of Hudson’s crew became the first man killed by Native Americans who were frightened by his scouting party.
There is no citation for this in the Wikipedia page, unfortunately. I'm interested to know if this is true, and, more broadly, if there is any information available about the relationship between these groups in this area. I know this may be a bit narrow as far as questions on this subreddit go, but if anyone has any sort of knowledge about this, I'd so appreciate it!
1609 is pretty late in terms of European contacts with Native Americans. Cortez had already fought a war with the Aztecs 80 years earlier.
I believe the first European documented to be killed by a Native American was Thorvald Eriksson, brother of Leif Eriksson, who the Saga of the Greenlanders states was killed by a Native American while leading the second Icelandic expedition to Vinland (Newfoundland).
Earlier claim: http://www.roadsideamerica.com/story/14155 " The name of the plaque-worthy dead Spaniard isn't mentioned. All that's revealed is that he was killed by arrows fired by the Caloosa tribe, either in late May or early June, 1513. Millions of white men have died in America since him, but he was the first."