RTFA: http://en.wikipedia.org/wiki/Stellar_engine

One of the simplest examples of stellar engine is the Shkadov thruster (named after Dr. Leonid Mikhailovich Shkadov who first proposed it), or a Class A stellar engine.[1] Such an engine is a stellar propulsion system, consisting of an enormous mirror/light sail - actually a massive type of solar statite large enough to classify as a megastructure, probably by an order of magnitude - which would balance gravitational attraction towards and radiation pressure away from the star. Since the radiation pressure of the star would now be asymmetrical, i.e. more radiation is being emitted in one direction as compared to another, the ‘excess’ radiation pressure acts as net thrust, accelerating the star in the direction of the hovering statite.[2] Such thrust and acceleration would be very slight, but such a system could be stable for millennia. Any planetary system attached to the star would be ‘dragged’ along by its parent star. The sun: power = 3.85*1026 W, force = 1.28*1018 N, mass = 1.99*1030 kg, acceleration = 6.45*10-13 m/s2. 1000000 years = 3.16*1013 s, velocity = 20 m/s.

Nice! Barring the current issues with human “death,” this would make it a lot easier to communicate with other life forms. Simply drag your star, and the solar system with it, to a reasonably small light-distance near to the life to communicate with. …Time dilation… The act of taking a long nap - what’s several hundred million years? The sun has a good - what - 2 or 4 billion left before it goes “red giant,” right? “We” can just find another stellar engine when the current one (Sol, “the Sun”) is used up.