The show features 19 exhibits around the 105-acre garden in Derbyshire.
Lilas, by Dame Zaha, who died earlier this year, was originally created for the Serpentine Gallery at Kensington Gardens.
The exhibition also features work from artists from Spain, Portugal and Taiwan.
The sculptures will be on show until 30 October and members of the public can bid to buy them.
Some of the work for the exhibition, including Bruce Munro's piece Time and Again, has been created specifically for Chatsworth.
It was inspired by the house's success in growing some of the earliest Victorian water lilies after seeds were first brought to England from British Guiana in 1837.

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In Wayne Bennett's first competitive game in charge, England were pipped by one point to fall to defeat at Huddersfield's John Smith's Stadium.
The 17-16 loss, along with Australia's win over Scotland put hopes of reaching the final in doubt, although there are still two matches to play.
"It's only the first game of the tournament," the 28-year-old said.
"If we dwell on the bad things we won't do very well. We have to look at the positives, we have the right man in charge [in Bennett].
"This will take a day or two to get over, we have to focus, we did a lot of good things and we need to take that into next week."
One positive of Saturday's loss was the continuation of the Leeds Rhinos man's terrific scoring record, crossing for his 29th international try in 29 games.
Hall has the opportunity to take his tally to 30, five more than Sam Tomkins and extend his lead as the top scorer in England Test history.
"Its bittersweet," Hall added to BBC Sport. "It was a great assist from Gareth Widdop, but ultimately the bigger picture stuff, that we lost the game is hard to take.
"It's fine margins, that's Test match rugby and the most disappointing thing is that we had enough to win the game."
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Her Majesty, who had been staying at the Palace of Holyroodhouse, popped into the Sheep Heid in Duddingston on Friday.
The Monarch had earlier been at Musselburgh Racecourse's 200th birthday celebrations.
She is very rarely seen eating out at public restaurants, but the 650-year-old Sheep Heid Inn has been linked to the Royals since the 1500s.
In 1580, King James VI of Scotland gifted the landlord an ornate ram's head snuff box.
It is believed he, and his mother Mary Queen of Scots, stopped by the inn many times to play skittles in the courtyard.
As a mark of gratitude he presented the landlord with the unusual gift which remained on site for 300 years before being sold at auction to the Earl of Rosebery.
A Sheep Heid spokesman said: "I can confirm the Queen was here. " He refused to give details on what she ordered.
However, it has been reported that the Queen and her companions enjoyed two portions of lamb and a fillet of seabass.
An "architecturally ambitious" piece by Zaha Hadid is to be included in this year's Chatsworth House sculpture exhibition.
[NEXT_CONCEPT]
England must take the positives from Saturday's Four Nations opener defeat by New Zealand, says winger Ryan Hall.
[NEXT_CONCEPT]
The Queen has been spotted having an evening meal at an Edinburgh pub.