When Ripley showed up to the planet in the first film, it's obviously a skeleton of an engineer in the captain's chair of the old ship with it;s chest broken apart (Not that exact ship, obviously, but similar) that we saw in Prometheus. This can make obvious sense going down the line for the first Alien movie. David messed around with shit and we saw what is the first incarnation of the alien as we know it with the face hugger, and what comes out. Now, he has a colony ship with 2k people on it and is heading out with 2 face hugger embryos in storage. I am guessing one of these would be a queen.
Now I am not too sure what will happen in the next two movies, but what I can see happening is by the end of the last movie of the trilogy, (A few years from now obviously) David infects an Engineer who then as a result, the engineer flying the ship (Possibly towards Earth) later crash lands on LV426 before the first Alien movie for reasons unknown as of yet, and eggs that Ripley finds is a result of the queen coming from the infected Engineer. Also, the Queen could have ALWAYS been alive from the first Alien movie and we wouldn't even know. They were on the planet and ship for only a fraction of time in the first movie, and in the second, the queen could have very well been alive the entire time, and once the colonists found the eggs and were infected to spawn Xeno's all over the place, the Queen came out and started reproducing more eggs.
Regardless, an Alien spawned from the chest of an engineer in the first Alien movie now that we know what that looks like from Prometheus. Logic would assume a Queen was spawned to lay all the eggs.
Remember, this is from the VERY first Alien movie when the crew first arrived on LV-426 and explored the ship before Kain got infected.