To sneak onto the TTC (Toronto Transit Commission) without paying. Originated from the song 'Baby Buluga' by Raffi as the extended jam (I know you've heard that one) contains a reference to stealing a ride.
"Baby Beluga in the deep blue see,
He snuck on to the TTC for free"
- Raffi (1980)
Recently the definition has been expanded to include stealing anything under $3.25 (the cash fare to ride the TTC).
Adam: Ugh. I don't have any change for the TTC. I guess I'll have Beluga Whaling it today. (Original meaning)
Adam: I don't have a pen. I guess I'll have to go Beluga Whale one from Stacy in accounting (new modified meaning)