It can only be exchanged for Game Chips during the Renzo Travelling Fair Mini-Event, you'll find it in your inventory:
Dragon Egg placed on your farm:
Time of incubation: 168 hours
Can also be shortened to just: 1 hour (see Egg Warmer explanation in 1st post)
When the Dragon is "ready to hatch":
Dragon egg transforms into Pet Dragon, and gives 20% EP for your whole farm, for 20 minutes.
Time between harvests: 10 hours
Size: 1x2
You can have a maximum of one item per field.
Source: Official Farmerama Forums.