They are able to bring the lawsuit because between Aug. 31, 1987 and March 29, 1993 there was no collective bargaining agreement between players and the organization.
Hundreds of former players are eligible to join the lawsuit. They have until the end of the year to add their name to the list of plaintiffs.
At the news conference Tuesday, Martin said he did research before contacting the attorney.
"People think that football ends when the player leaves the field. But now we're learning that football is not going to end until you're in the grave," Martin said.
Martin has been diagnosed with dramatic brain injury and post-concussive syndrome.
"I would like to have had the opportunity to know that going back on the field would cause me to have severe disabilities in life," he said. "I didn't know that. I think that's what the lawsuit is about."
We reached out to the Chiefs and they told us there have no comment at this time.