Carbonating in the Carboy?

Is it possible for a beer to carbonate while in a secondary? Mine appears to have.

Here's the situation... I recently brewed a 1.080 Belgian Ale and fermented it in a 6.5 gallon glass carboy. After 3 1/2 weeks, the gravity dropped to 1.019, so I transferred it to a 5 gallon carboy. I made enough to completely top off the carboy, so there was only about 1/4 inch of space between the beer and the stopper. It's now been 6 weeks and it's always been continuously bubbling in the secondary (once every 12-15 seconds). I checked the gravity today and it's down to 1.012. It seems to be pretty well carbonated. Do you think this was because of a near total lack of oxygen? Should I prime as usual when bottling?

Many thanks, guys!

You have co2 in solution, but that doesn't mean your beer is carbonated. Co2 is a byproduct of fermentation, it's present all the way through the process. But you need to actually force it under pressure into solution for a beer to be truly carbonated. Just relax, and bottle as you normally would.

yes prime as usual. the co2 is escaping, not staying in the beer.

How cold is the room where it has been sitting

Thanks for the info, guys!

@dnslater The room is not very cold. Fermenter temp says 72. Normally, I keep my carboys chilled lower, but the yeast strain for this belgian is up to 75 degrees.