Syzygy
"Wait, what?" you ask. Well, it's the only English word with 3 Ys. Remember in grammar school: A E I O U & Sometimes Y? Well, in this case it's A E I O U and this time, only this time, 3 times Y. And, no this is not algebra! :(
"Weird," you say? Well, consider the definition:
The nearly straight-line configuration of three celestial bodies (such as the sun, moon, and earth during a solar or lunar eclipse) in a gravitational system.
So, not only is the word a rarity, but the event it describes is one, too. :)