From my experience all animals act differently. I've had pets go into a sort of "depression" after their mate/friend has passed away. But they have seemed to bounce back out of it (though slightly changed) after time and lots of love. On the other hand, I've had animals notice the other was gone but not necessarily be affected by it at all. See how the other one does on it's own. Because chances are getting another one to be it's "friend" may not work out and they may not get along (plus it takes a lot of time and patience to introduce two chins, you can't just put them together right away). Then you'll have two who need extra love.

If it were me, I'd probably wait and see how the one reacted and be sure to give it some extra love and attention. And go from there.
I'm sure others will have other personal experiences, too!