Well, I had my crystal version stolen a while back, so I may be wrong, but... I think you are referring to a second egg that is obtained. On crystal you recieved one egg from Violet City, which hatches into a Togepi. I believe there is a second egg obtained, at the daycare, which hatched into either a Magby, Elekid, Smoochum, or Cleffa, along with the move Dizzy Punch and a 50% chance of being a shiny... Of course, like I have stated, I haven't played crystal in a long while (I've recently downloaded the ROM, but I'm only in Violet City), and my memory can fail me at times... So maybe there isn't a second egg... Hmmm... :\
However, I do remember owning an egg which hatched into an Elekid, and another file in which it hatched into a Smoochum. On the file I had before my game was stolen, my egg hatched into a Shiny Cleffa :D
But yeah, I can't even tell if I'm on-topic anymore... I'm pretty sure there was a second egg though, however I do not know if there was one in Gold/Silver (I played Crystal, which had quite a few changes).