The 28-year-old raptor, affectionately named Lady by rangers at the Loch of the Lowes nature reserve near Dunkeld, Perthshire, returned to her nest at the end of March for a record 23rd year.
She broke more records last month by laying four eggs, one of which hatched on Saturday.
The tiny, fluffy grey chick surprised reserve rangers by taking just one hour to break through its shell.
If the chick survives and successfully leaves the nest, it will be Lady’s 50th chick to have fledged – double the average number an osprey sees leave the nest in her lifetime.
It is unknown how many of Lady’s eggs have hatched in her lifetime but she has had 49 chicks leave the nest.
Rangers at the reserve, which is run by the Scottish Wildlife Trust, had been anxiously waiting the chicks arrival.
Val Gall, wildlife interpretation officer, said: “It is just fantastic. The staff here are all over the moon.
“There were shouts of ‘yes’ when the chick broke through and we are all celebrating.
“The fact that Lady is the age she is and has produced a live chick is just amazing.
“We now just have our fingers crossed that this chick will survive and fledge and become our golden egg as Lady’s 50th fledgling.”
Ms Gall added: “The ospreys will continue to incubate the other three eggs.
“The egg that has hatched has a significant amount of yolk in it so the chick survives on that before the ospreys start feeding it.”
Ranger Emma Rawling said: “We think this is probably egg number three hatching on time, rather than egg number two being late, but as the eggs are so hard to tell apart, we will have to wait and see if any of the others hatch to be sure.”
The chick has already been fed twice by its mother, with tiny amounts of shredded raw fish.
Ms Rawling said: “We can see the female has stashed some fish, tucking it under her whilst incubating , to ensure there is plenty available to give the chick little and often meals.
“The chick looks strong and healthy, with its instinct to reach up for food just as it should be. It is absolutely normal for new hatched chicks to find it difficult to lift their heads up and have poor balance.
“We hope it might be joined in time by another sibling, but for now we are simply overjoyed with one healthy youngster on the nest.”
Lady’s mate, known as Laddie, is younger than Lady. He is her fourth breeding partner in 22 years, and has fathered several of her previous chicks.
It had been feared that Laddie’s inattentiveness might have compromised the ability of Lady’s eggs to hatch – he twice left them to cool when he was on sitting duties this year.
Lady has an army of fans throughout the world, who monitor her progress via a nest-cam and online blog.
Laddie and Lady produced one chick last year which was named Blue.
Ospreys became extinct in England 1847 following widespread persecution for their feathers and habitat loss. They were wiped out in Scotland by 1916.
However, the species has gradually returned thanks to a re-introduction scheme south of the Border in the late 1990s and natural recolonisation of Scotland from 1954.