The bird, known as Lady, laid the egg at Loch of the Lowes reserve near Dunkeld, Perthshire, yesterday morning.
The laying of eggs is generally separated by a couple of days so more could be on the way, the Scottish Wildlife Trust said.
On average, osprey incubation lasts between 37 and 39 days, so the earliest hatching would be on May 20.
The Trust believes Lady is 28 years old and she returned to Scotland as usual this spring after spending the winter in Africa.
Last year, she watched her 50th chick fledge from her nest at the reserve.
Park ranger Emma Rawling said staff are "overjoyed" and delighted she is still breeding.
"It has come just as the Trust is celebrating its 50th anniversary, so it is almost like she knew that it was a special occasion and wanted to make it extra special," she said.
"Now there is a tense wait to see if there are any more eggs to be laid this season. This osprey never ceases to amaze, so it is certainly a possibility."
The Trust said the day the egg was laid had been eventful.
Hundreds of people visited the reserve to see the bird but Lady fled her nest when two people got too close.
An entry on the Loch of the Lowes blog, which regularly provides updates on the osprey, said: "She was away for quite a while, and even on her return, she was unsettled and didn't resume incubation for another 10 minutes.
"We are so very lucky that in this period an opportunistic predator didn't happen by, and that the weather was gloriously warm so the egg is unlikely to have suffered any damage.
"What caused the disturbance was the irresponsible actions of two people who walked into the small area of the reserve that is off limits this time of year to protect the breeding birds."
Egg collecting, hunting and a loss of habitat reduced osprey numbers across the UK in the early 20th century. The birds began to repopulate Scotland in 1954 when a pair of Scandinavian birds settled in the country.
The Scottish Wildlife Trust said the success of the Loch of the Lowes reserve was down to the hard work and dedication of staff and volunteers since 1969.
The Trust was established 50 years ago this week and manages over 120 reserves in Scotland.