I haven't seen The Great Dictator (a failing on my part I know) so I don't know exactly how Chaplin delivers this particular information. I can address however what he might have been referring to.

Deadly gas, or chemical weaponry, had been a major feature of the previous war. Hitler had experienced the effects of gas when he himself fell victim to it when he was serving on the Western Front. Though neither the Axis or the Allies used chemical weaponry in offensive warfare against each other, all sides were aware of the threat that chemical weapons posed, hence the distribution of gas masks amongst Allied and Axis soldiers as well as civilian populations. Chaplin may have been referring to the possible use of chemical weapons rather then the use of chemicals such as Zyklon B which here indeed not used until after the release of The Great Dictator.

The use of concentration camps in Nazi Germany had been a feature of the Third Reich since Hitler came to power in 1933 when Dachau was established. We associate concentration camps with places such as Auschwitz, Treblinka and Sobibor which were indeed concentration camps but were also used extensively as extermination camps. Camps such as Dachau were originally intended for the internment of political prisoners, homosexuals, communists and of course Jews. Dachau and the concentration camps that were established prior to the Wannsee Conference were not intended extermination as extermination camps but rather as labour camps and as a means of removing individuals and groups that were perceived as threats to the Reich from the general population. The existence of concentration camps prior to 1940 was known by international communities though how widely I do know.

Chaplin, as well as most people who paid attention to international affairs, would have been well aware by 1940 of the persecution of Jews in Nazi Germany. The most obvious evidence of US awareness of the persecution of Jews before 1940 is the Wagner-Rogers Bill which sought to amend the quota of immigrants to the United States in order to allow Jewish children fleeing persecution in Germany entry to the United States. This was in direct response to Kristallnacht, the Night of Broken Glass, when Jews and Jewish businesses in Nazi Germany were targeted by Nazi party supporters.

tl;dr I haven't seen The Great Dictator but I speculate that Chaplin was not indicating knowledge of the Holocaust in the film but rather referring to three seperate features (or possible features in regards to chemical weapons) of Nazi Germany that when listed together, can sound as though he were referring to three features of the Holocaust.

To add a bit to /u/TheWellSpokenMan 's answer: I have written before on what the Allies knew of the Holocaust and what's important here is that while the world was well aware of the persecution of Jews in Nazi Germany with events such as the November pogrom in 1938 and the Evina conference about Jewish emigration from Germany, the Holocaust as in the the systematic mass murder of Jews didn't start until 1941.

I deal with this in-depth in this answer but the gist is that it was only when the Nazis invaded the Soviet Union that they started murdering Jews systematically and en masse. Before that Jews were forced into ghettos (featured strongly in Chaplin's film), oppressed, and forced to live under horrible conditions as well as killed on occasion but the program of wholesale murder came only about in 1941.