The falcon family are nesting at the top of county hall and the female laid two eggs between March 25 and April 5.
A chick hatched this week and it will be around five to six week until it begins to fly.
However, it is unlikely there will be a second falcon chick this spring as the hatching should have occurred by now, according to Aylesbury Vale District Council’s biodiversity team, which is monitoring the peregrines.
Councillor David Thompson, cabinet member for leisure, said: “It is wonderful that Aylesbury’s peregrine falcons have successfully bred again this year.
“It is so exciting for people walking through the town centre to look up and get a sight of the birds.”
Since the birds of prey returned to Aylesbury earlier this year, more than 10,000 hits have been recorded on the council’s website.
Anyone can view live footage from the platform on the website and the council is hoping to arrange events to help people get the best view of the family.
The peregrine project is supported by volunteers and the web streaming is paid for by donations from the public and other organisations.
If you would like to help call the biodiversity team on 01296 427972.