Greene most likely saw this claim being made by Yasha Levine, a writer for the The eXile. He writes:
During the 1968 protests of the Democratic National Convention in Chicago, which drew about 10,000 protesters and was brutally crushed by the police, 1 out of 6 protesters was a federal undercover agent. That’s right, 1/6th of the total protesting population was made up of spooks drawn from various federal agencies. That’s roughly 1,600 people! The stat came from an Army document obtained by CBS News in 1978, a full decade after the protest took place. According to CBS, the infiltrators were not passive observers, monitoring and relaying information to central command, but were involved in violent confrontations with the police.
Levine cites a 2008 book entitled Battleground Chicago: The Police and the 1968 Democratic National Convention, by Frank Kusch. But the book does not unambiguously back up his statement.
A CBS Television News special broadcast in 1978, attributed to unnamed army sources, claimed that during convention week "about one demonstrator in SIX was an undercover "68 Furthermore, CBS contends that on Wednesday night, at least 200 of agent. those that blocked tramc and skirmished with police along Michigan Avenue were undercover agents. The revelation prompted Todd Gitlin to ask, "Just who wanted blood to flow in Chicago, and why? "
Former officers scoff at such an allocation of resources by any government agency, especially the numbers attributed to CBS. Says Randall Bakker, "That doesn't make any sense—there were six to ten thousand punks on the streets doing battle during that time. If that report is right, there would have been 1,000 to 2,000 agents, at least, dressed in hippie garb fighting us outside the Hilton." Orrest Hupka agrees, "It's absolute nonsense," says the officer who worked in plainclothes near the Hilton the entire week. "People say that these phantoms were there to fight us so we would fight them back and kill the movement? How does that work? Force our hand against thousands of cops and undercover agents. These conspiracy theorists." Police suggest that such a level of cooperation with government agents from Washington would have been difficult, as they would not have been able to differentiate between a real protestor and a government agent. "There were rumors that some of the hippies were actually federal agents," says cop Steve Nowakowski. ' 'This made some of the guys swing harder at the crowd."
Levine did not make mention of the skeptical cops -- I guess cops lie but "unnamed army sources" don't. The CBS reporter might have been misunderstanding an army source saying that there were 1000 Secret Service and FBI agents on duty during the protest, presumably barricading the DNC building with the police.
The original CBS special is available on YouTube and features an interview with a single undercover agent who points himself out in a crowd. But they don't ask the agent if there were others like him, or if he fought with the police. He tells the cameras that he was there to gather evidence for the Chicago Seven trial, not to exacerbate the protest. The CBS video also shows that Levine is incorrect when he cites an "Army document," as there was no document mentioned or shown.
Battleground Chicago does offer a more specific claim about police infiltration. However, the claim is not that police infiltrated the hippies, but rather that police supplied weapons to right-wing extremists who wanted to stop the left-wing protest.
Though most reports suggest that such agents were only undertaking "routine" surveillance, there are indications that the efforts went deeper. As far back as 1970, the Washington Star reported, "plainclothes military intelligence agents played a questionable —and still secret— surveillance role at the 1968 conventions." The Star indicated that the U.S. Secret Service borrowed agents from the 113th Intelligence Group based in Illinois that were engaged in intelligence operations on the streets of Chicago.
Furthermore, there are suggestions that this sharing of domestic intelligence officers included a constant exchange of information between the 113th group and members of Chicago's Red Squad. George O'Toole, a former chief of the CIA's Problems Analysis Branch, maintains that this contact was more than peripheral. The Red Squad was in daily contact with the army's 113th Military Intelligence Group during the late 1960s and early 1970s, passing along intelligence reports and receiving a variety of technical assistance. The 113th also provided money, tear-gas bombs, MACE, and electronic surveillance equipment to the Legion of Justice whom the Chicago Red Squad turned loose on local anti-war groups.
While the use of weapons is surprising, this is a much more logical claim in terms of end goals. The police were opposed to a disruptive protest and wanted to forcibly separate it from the DNC, shut it down, and arrest its leaders. They would have had nothing to gain from sending cops to fight other cops. As this book notes, counterprotest tactics were standard operating procedure for police and FBI in those days, and have been at more recent political protests as well. (The CBS special also has a video with one of these 113th agents.)
Greene's claim is based on a real claim by CBS; but the claim was not originally so strong, was contested from the start, and runs counter to the ordinary logic of government intervention into political protests.