How is Prometheus connected to Alien vs. Predator in the chronological sense?

Question

At the end of Prometheus, we saw that a creature was born from the body of the dead Engineer which was essentially identical to the Alien creature pictured the Alien vs. Predator movies (a Xenomorph).
Now my question is how are they connected chronologically? I imagine that the AVP happen in the present time but Prometheus is dated in the future.

Answer 1

From the Prometheus IMDb FAQ:

It should be noted that AvP franchise is not considered part of the official canon of the Alien saga [...]

Prometheus is considered by both Ridley Scott and the film's producers to be the first film in the Alien series.

From an interview with Damon Lindelof:

[...] Look, as to what’s canon and what’s not canon, for me as a screenwriter it’s transcended by Ridley as a director.

Here’s the thing. Ridley invented this. He created this Alien universe. He birthed it out of his own heart and soul. So he gets to do whatever it is he wants to do and he wanted to use Weyland as a conduit in the story, and was not interested at all when I said to him, “You know, Weyland was a character in one of the Alien Vs. Predator movies,” he just sort of looked at me like I had just slapped him in the face. That was the beginning, middle and end of all Alien Vs. Predator references in our story process.

Answer 2

I am not a movie writer but I must say when watching the Prometheus movie I thought I seen a connection to Predator and Alien as well.

If you remember back to the part were the one crew member was infected and then started to feel sick and started to change and then they torched him out side the ship.

Well if you recall after that when they went to check because they thought he was still alive but by then he had changed completely and looked more humanoid like how the Predator looks.

If you recall his facial features and the beyond normal human strength just wanted to throw that thought out there.

Answer 3

As Wikepedia says -

Prometheus was originally intended as a direct prequel to the 1979 science fiction horror film Alien, set approximately 30 years before the events depicted in the film. While the finished film explored a more stand-alone mythology based upon the race of giant beings discovered by the crew of the Nostromo in Alien, it is, as acknowledged in the end credits, based on elements from the original film.

As stated in Alien vs. Predator Wikepedia page

In a 2002 interview, Scott's concept for a story was "to go back to where the alien creatures were first found and explain how they were created"; this project eventually became Scott's 2012 film Prometheus. On learning that Fox intended to pursue Alien vs. Predator, Cameron believed the film would "kill the validity of the franchise" and ceased work on his story, "To me, that was Frankenstein Meets Werewolf. It was Universal just taking their assets and starting to play them off against each other...Milking it."[38] After viewing Alien vs. Predator, however, Cameron remarked that "it was actually pretty good. Cameron remarked that "it was actually pretty good. I think of the five Alien films, I'd rate it third. I actually liked it. I actually liked it a lot."[38] Conversely, Ridley Scott had no interest in the Alien vs. Predator films. When asked in May 2012 if he had watched them, Scott laughed, "No. I couldn't do that. I couldn't quite take that step.

Its clear that Ridley Scott never in a favor of Alien vs. Predator Franchise and that's the reason that his film Prometheus only connected to Aline Franchise only , it doesn't have any connection to Alien vs. Predator films.

As stated in Prometheus Wikepedia link

Development of the film began in the early 2000s as a fifth installment in the Alien franchise. Scott and director James Cameron developed ideas for a film that would serve as a prequel to Scott's 1979 science fiction horror film Alien. By 2003, the development of Alien vs. Predator took precedence, and the project remained dormant until 2009 when Scott again showed interest. Spaihts wrote a script for a prequel to the events of the Alien films, but Scott opted for a different direction to avoid repeating cues from those films. In late 2010, Lindelof joined the project to rewrite Spaihts's script, and he and Scott developed a story that precedes the story of Alien but is not directly connected to that franchise. According to Scott, although the film shares "strands of Alien's DNA, so to speak", and takes place in the same universe, Prometheus explores its own mythology and ideas.

So its clear that Prometheus is a sequel to first alien film and their may be one more Prometheus film which will fill the gap between First Alien film and Prometheus and AVP's is just like a Spinoff.