30 December 2014 Last updated at 14:11 GMT
Keepers have named the female Rothschild's giraffe calf Zahra, which means 'flower' in Swahili.
The 1.8m tall calf was born to mum Aiofe and dad Meru.
Rothschild's are one of the world's most endangered sub-species of giraffe, with experts predicting that there are less than 1,100 left in the wild.
"We're happy to report that our new, not-so-little, youngster is doing well and is already confident on her long legs," said Tim Rowlands, the curator of mammals at Chester Zoo.
The zoo now has a herd of eight Rothschild's giraffes - Meru, Aoife, Dagma, Orla, Tula, Kanzi, Millie and Zahra.

Oliseh, 41, had been in the job for only eight months.
Nigeria have installed Samson Siasia to oversee next month's crucial 2017 Africa Cup of Nations qualifiers against Group G leaders Egypt.
"Your contractual violations and the interest of the nation necessitates that I tender my resignation," he wrote to the Nigeria Football Federation.
"So little help is being rendered me in getting the players to give their best and very vital conditions and advantages to the team play are also being sacrificed... my several e-mails and others seeking your aid to effectively carry out my duties were ignored."
The NFF technical director Shaibu Amodu, who has managed the national team on four occasions, is widely expected to take charge of the team on a temporary basis.
Former Nigeria captain Oliseh endured a turbulent reign as Nigeria boss after succeeding Stephen Keshi in July 2015.
Some high-profile players have retired, including goalkeeper Vincent Enyeama - Nigeria's most-capped player, who quit after he was replaced as captain.
Two weeks later striker Emmanuel Emenike also announced his retirement from international football.
In early February, a frustrated Oliseh posted an eight-minute video rant on his own website to hit back at what he called the "insanity" of his critics.
He had come under pressure after Nigeria failed to get past the group stages of the 2016 African Nations Championship (CHAN) in Rwanda.
The coach later apologised to the NFF for his outburst aimed at the Nigerian media as well as some of his former international team-mates.
Oliseh had also gone public with the money problems affecting his team during the continental tournament in Rwanda, to the embarrassment of his employers.
Nigeria face seven-time African champions Egypt in back-to-back 2017 Nations Cup qualifiers next month.
They are two points behind group leaders Egypt after two rounds of matches with only group winners guaranteed automatic qualification to the tournament in Gabon.

Police Scotland said no-one was injured in Tuesday's incident.
A spokesperson for Police Scotland said Inverness Community Beat officers dealt with the matter.
The officers will be working with staff at the school, which has not been named, over the next few days "to provide reassurance to all involved".
Visitors to Chester Zoo are getting their first glimpse of a rare baby giraffe born just before Christmas.
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Sunday Oliseh has resigned as coach of Nigeria citing contract violations, unpaid wages and lack of support.
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Police were called to a school in Inverness after a pupil was found with a knife.