Mr Owen said that "around-the-clock care and attention are needed to rear these tiny and delicate birds".
It was hoped that the doves, once mature, would start to breed in their purpose-built aviaries at Parque das Aves, he added.
Paloma Bosso, technical director of Parque das Aves, said it was "a joy and also a great responsibility" to see the three chicks.
"Each hatching represents a real chance to reverse the fate of this species," she said.
Parque das Aves is now home to six blue-eyed ground doves.
The species is critically endangered according to the International Union for Conservation of Nature Red List.
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