The Mote in God's Eye

In 3016, the 2nd Empire of Man spans hundreds of star systems, thanks to faster-than-light Alderson Drive. Intelligent beings are finally found from the Mote, an isolated star in a thick dust cloud. The bottled-up ancient civilization, at least one million years old, are welcoming, kind, yet evasive, with a dark problem they have not solved in over a million years.