The chicks are the latest brood for the pair of Peregrine Falcons that have lived in a bell tower of the Antoni Gaudí-designed church since 2004.
The birds' mother is sticking close to the youngsters but was unperturbed by the presence of scientists who checked up on the brood recently, local daily La Vanguardia reported on Friday.
The father was less keen on having visitors, keeping a close eye on proceedings, the scientists told the paper.
The falcon hatchlings will be fed on a diet of pigeons, starlings and other birds. Their hunger is unlikely, however, to put a dint in the overpopulation of pigeons at the unfinished church, La Vanguardia said.
There are thought to be some 12,000 pairs of Peregrine Falcons (Falco peregrinus) in Europe, according to National Geographic.
This includes populations at iconic buildings like the Notre Dame Cathedral in Paris and the Tate Modern in London.
But the eggs of these birds contain 100 times the legally permitted pesticide levels for hen eggs for human consumption.
Peregrine Falcons are reportedly the fastest birds in the world and one bird was clocked by National Geographic at 389kph (242mph).