Somewhere between February and March, and our own sources do not fully agree on where. The wildlife research puts Adélie fledging often in February and chinstraps from February into early March. Our guides, talking about the colonies they actually work, put fledging in March with first swims late in February. Gentoos are the least predictable of the three either way, and vary a lot by colony and latitude.
We would rather tell you that than pick a month and sound certain.
Fledging means the chick has swapped its insulating down for waterproof juvenile feathers and starts going into the sea on its own. The first entries are hesitant and slightly chaotic, and they are the reason leopard seals hang around water entry points at that time of year.
A whole colony does not fledge at once, and the colonies on one voyage will not all be at the same stage. Weather, food supply, breeding chronology and local conditions all pull the timing around, and two colonies you visit on consecutive days can look completely different.
The stage before this one is the crèche, where chicks gather together in groups. That is a February scene at many sites: large, mobile, half-moulted chicks, feather development well along, and heavy traffic between the colony and the sea.
If a specific stage matters to you, say so when you book. It maps to a departure window better than most things people ask about.