The chicks are born of Laysan albatross parents. Albatross mate for life -- or at least, so long as each partner comes back to the island each year. So what is particularly interesting about these cup-of-sugar neighbors is that they aren't the first albino chicks to be born from these parents. According to a USFWS newsletter from 2010, albino chicks have been seen in the same area 3 of the previous 4 years. So the same two mated Laysan albatross pairs carry genes that result in albino chicks, and the pairs have continually hatched them.
The odds of two pairs consistently producing albino chicks are fairly slim, and that they've chosen nest sites so close to each other makes this a rather extraordinary neighborhood.