The Team USA gymnast was initially given a bronze in the women's floor event at the Games after an appeal regarding how the judges scored her routine was successful on the day, but this was subsequently overturned by the Court of Arbitration for Sport (Cas) - handing a place on the podium to Romania's Ana Barbosu instead.
Barbosu and her team appealed to Cas, usually regarded as the highest authority on legal matters in sport, that Chiles' inquiry had been filed four seconds after the one-minute deadline under International Gymnastics Federation (Fig) regulations and ultimately proved successful.
It is Chiles' latest legal bid to get the medal back after she already had two appeals rejected by Cas.
Her lawyers argue that the court refused to consider video footage that "unequivocally proves" that the inquiry was submitted within the time limit.
USA Gymnastics wrote in a statement on Monday (16.09.24): "(We made a) collective, strategic decision to have Jordan lead the initial filing. USAG is closely coordinating with Jordan and her legal team and will make supportive filings with the court in the continued pursuit of justice for Jordan."
Chiles revealed last month that she has suffered racist abuse on social media as a result of the "unjust" decision to take away her medal.
In a statement posted on X: "To add to the heartbreak, the unprompted racially driven attacks on social media are wrong and extremely hurtful.
"I've poured my heart and soul into this sport and I am so proud to represent my culture and my country."