The government said Newman, 46, and Chiasson, 49, traded on tips they received from analysts who worked at their hedge funds.
These analysts, the government said, were part of a "corrupt circle" of investment firm analysts that traded non-public information obtained from insiders at various companies, including Dell and Nvidia.
Newman has been sentenced to 4-1/2 years in prison, and Chiasson faces a 6-1/2 year term. Both men have been free on bail pending their appeal.
A ruling reversing Newman and Chiasson's convictions would mark a significant setback for Manhattan U.S. Attorney Preet Bharara, whose office has secured insider trading convictions of 80 individuals since October 2009.
The U.S. Supreme Court in 1983 held that a "tippee" can only be found to have engaged in insider trading if the tipper benefited from the disclosure.
The issue the 2nd Circuit is being asked to address is whether prosecutors must show the tippee knew of the tipper's benefit, which can be financial or non-monetary.
Read More HFT isn't the problem—insider trading is: Op-ed
"It's a significant question both in terms of giving guidance to the business community and in terms of whether prosecutors are trying to stretch the securities laws too far," said John Buretta, a lawyer at Cravath, Swaine & Moore who is not involved in the case.
At Newman and Chiasson's 2012 trial, U.S. District Judge Richard Sullivan in Manhattan declined their lawyers' request to instruct the jury that for the men to be found guilty, prosecutors needed to prove they knew the insiders benefited.
He gave a similar instruction in the case of Michael Steinberg, a SAC Capital portfolio manager convicted in December in a case that involved the same alleged "corrupt circle" of analysts.
Newman and Chiasson's lawyers contend that Sullivan misconstrued the law. In appellate briefs, the lawyers cite rulings in which four other judges from Manhattan federal court came to the opposite conclusion from Sullivan.
Defendants in those cases include Galleon Group hedge fund founder Raj Rajaratnam, SAC Capital portfolio manager Mathew Martoma, and California hedge fund manager Doug Whitman.
Stephen Fishbein, a lawyer for Newman, told the 2nd Circuit during arguments over bail in June that whether his client faces jail "should not depend on what judge we drew and where that judge comes down on a hotly debated issue that the courts haven't decided."