##Eliminate their motivation##

(This meant as a compliment to [separatrix](http://worldbuilding.stackexchange.com/users/16295/separatrix)'s answer.)

**No fear of extinction**

In addition to the Cold War and the space race, we also have the fear of a future cataclysmic event. Some scientists are worried that if the Earth is struck by a big enough piece of space debris, or if we have a global thermonuclear war, our species will cease to exist. Their solution to this fear is to spread the human race to other planets and other habitable places in space.

Earth has a major extinction event in its past. If the planet where your alien civilization is has never had a major extinction event, and has never had weapons capable of destroying the entire population, then they have no reason to fear that their species could be wiped out. This eliminates the desire to spread the species out in order to prevent the risk of extinction.

**Stable population size and resources**

Another reason we might want to leave Earth is that our population is continuing to grow and consume more and more resources. We may yet be a long way off from using up all our natural resources and running out of room, but we're close enough that we're worried about it being a problem in the future. Spreading out to the stars is a solution.

If your aliens have already developed sustainable energy sources and eliminated all significant reliance on limited resources, then expanding to other worlds to obtain more resources isn't an issue.

If your aliens have reached a stable 1:1 birth:death ratio, then population growth isn't an issue either. Interestingly, humans are trending towards that already.