The International Association of Athletics Federations (IAAF) banned Russia's entire track and field federation following revelations of massive, state-sponsored doping.
The suspension first announced in November was maintained last month, which appeared to all but crush Russia's hopes of sending athletes to the Games in Rio de Janeiro, which open on August 5.
But the announcement from CAS offers yet another last chance for Russia's disgraced track and field programme.
"The parties have agreed to an expedited procedure which should conclude on 21 July 2016," the statement added.
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Qualification for most athletics events closes on July 11.
But with the Russian case under intense public scrutiny and facing political pressure from Moscow, the IAAF may retain some flexibility to extend key deadlines.
- A new twist -
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The IAAF ban followed a November report from the World Anti-Doping Agency which said Russia's track and field programme had been corrupted to the point where even clean drug tests were meaningless.
The issue in the CAS appeal is whether the IAAF has
grounds to suspend an entire athletics team, given that such a move invariably results in punishments for individuals with no positive drug tests on their record.
Hogg said the court's decision will be narrowly focused on the validity of IAAF competition rule 22.1 which holds that "athletes whose National Federation is suspended by the IAAF are ineligible for competitions."
Russian officials have blasted what they call the IAAF's hypocrisy, noting that two American celebrity sprinters -- Tyson Gay and Justin Gatlin -- will be among a series of athletes competing in Rio who have previously tested positive for doping.
- IOC confusion? -
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International Olympic Committee executives last month said the IAAF had full authority to decide on which athletes can contest in Rio.
That was at odds with the IAAF position: the governing body said that athletes who individually proved they were drug free could compete under a neutral flag, as the Russian track and field federation would remain banned.
Several Russian track and field stars have already filed petitions with the IAAF to establish their drug-free credentials.
But if CAS overturns the blanket ban, those individual petitions could be rendered meaningless.
The court did not provide a list of the 68 athletes involved in the case, but it likely includes most potential Olympians with no positive drug tests on their record.