Since the stay was granted, little news about progress has been made public.
In the meantime, the tribe has added an experienced, Washington, D.C.-based attorney to its team of lawyers.
Douglas Endreson was granted permission to argue before the federal judge presiding over the case at the end of April, records show.
Endreson's profile on his law firm's website says he has extensive experience in tribal issues, including gaming, hunting and fishing rights, tribal taxation and water rights.
A task force, which includes the top officials of the Chickasaw and Choctaw nations, was formed earlier in the month to facilitate negotiations between the two sides.
The 19-member group was formed by mediator Francis E. McGovern, who also worked in the same capacity following the BP oil spill in 2010.
Finding a solution to Oklahoma's current water dispute is the sole function of the group and McGovern will give regular reports on the group's progress to the presiding judge.