Close, but not in the nest prior to fledging.
This membrane is a transparent third eyelid or haw that moves horizontally across the eye and keeps it moist and also keeps the dust out.
It is common in many animals including reptiles and birds and also present in camels and polar bears among other species.
They are being a bit more cooperative this morning.
postscript: actually you can see the feathers of number three in the left foreground. my bad.