9 May 2015 Last updated at 09:34 BST
Gentoo penguins tend to live in ice-free areas near Antarctica, and make special circular nest made out of stones, moss and feathers.
Their steam-lined bodies mean they can swim up to 22 miles and hour underwater, faster than any other diving bird.
Senior penguin keeper at the zoo Dawn Nicoll said: "We are really happy that the first of the gentoo penguin eggs have hatched".

The law, which is set to become a world first, aims to close the wage gap between men and women.
Companies face auditing and possible fines if they do not comply.
Iceland was ranked first in the World Economic Forum's 2015 Global Gender Gap Index, followed by Norway, Finland and Sweden.
However, according to Iceland's statistics for the same year, the unadjusted gender pay gap remained at 17%.
The bill, which was presented on Tuesday, is supported by the centre-right coalition government and the opposition.
Applying to both the public and private sector, it would prohibit any discrimination not just on gender, but also on race, religion, disability, occupational disability, age and sexual orientation grounds.
"The bill entails that companies and institutions of a certain size, 25 or more employees, undertake a certification of their equal-pay programmes," Thorsteinn Viglundsson, the minister of social affairs and equality, told news agency AFP.
The bill will now be subject to a series of debates, and if it passes, it will take effect from January 2018.
In Iceland's parliament, nearly 50% of lawmakers are women, and a voluntary measure for equal pay across the country was introduced in 2012.
However, many still do not think enough is being done.
In October, thousands of women left work early and headed out on to the streets of the capital, Reykjavik, to protest against earning less than men.
It echoed the 1975 Icelandic women's strike, when women did not go to their paid jobs, or do any housework or child-rearing at home for one day.

Glen Evans was left with a broken nose and his bride Georgina was punched at Fanhams Hall Hotel in Hertfordshire, St Albans Crown Court heard.
Lee Doyle, 37, of Houghton Regis denied punching the groom. He and Gary Hutson, 46, of Luton, both charged with affray, were guests at another wedding.
Both deny affray on 10 August 2014.
The court heard an argument broke out when Mr Doyle and Mr Hutson asked Mr and Mrs Evans and their friends to move away from a fireplace.
The newly married couple and their group were having drinks at the hotel following their own reception at another hotel.
Mr Evans said the two men and the other groom confronted him, saying the area was reserved, although his party had been put there by bar staff.
He said the two men hit him, and he was kicked and punched by others who joined in the attack. Mrs Evans was then also punched, leaving her with bruising to the head.
However, Mr Doyle told the court he was trying to defuse the situation, which he described as "volatile".
He admitted pushing Mr Evans and "grappling" with him as he thought he was going to attack Mr Hutson.
Mr Doyle described Mr Evans as "irate and aggressive" but denied hitting him.
Earlier this week Mr Evans denied allegations that he had thrown the first punch and had been "aggressive".
The trial continues.
Egg-cellent news the first gentoo penguins chicks have arrived at Edinburgh zoo this year.
[NEXT_CONCEPT]
Iceland's parliament is examining a bill that would require companies to prove they offer equal pay to employees.
[NEXT_CONCEPT]
A man accused of punching a groom when two wedding parties clashed at a hotel has denied hitting anyone but admitted "grappling" on the floor.