It is actually possible, though it would stretch the definition of "vest." It's not something that can really fit on a vest, but I suppose you could hide it in a fat suit, a wheelchair, or a fake pregnancy belly.
https://en.wikipedia.org/wiki/W54
The W54 was a 1 kiloton bomb that weighed a bit over 50 lbs. It was built to be a man-portable demolition charge. It's certainly possible for something like that to be built in a way that could be concealed on your person.