Well to make long story short Chetnics originally were Serbian fighters (guerrilla) AGAINST Germans. And against communists (most of the time) all though they cooperated from time to time against Germans. Looks like they cooperated from time to time with enemy against communists too (not sure about this). Murky times...They were royalists.
After the war against Germans (and civil war at the same time) Tito had to make balance between nations in order to make "brotherhood and unity" alive. That's why our history books equalized Ustashe (Croats Nazi force) and Chetnics both as same evil. But they were nothing like same at all. Sorry I am not in a mood to write long posts at the moment so I'll copy/paste few things from Internet that I found relevant:

The Royal Serbian army, better known as "the chetnics", under the command of general Draza Mihailovic, saved a total number of 513 American pilots during WW2.
...General Draza was awarded the Legion of Merit for his heroic deeds.
...Legion of Merit is the highest USA decoration meant for foreign citizens for exceptional merits. Draza Mihailovic was decorated at the proposal of USA General Dwight Eisenhower.
...Hollywood even made a movie during WW2 about the Serbian chetnics, which are today portrayed as some sort of animals that bite off people's ears and stuff...
...He did indeed earn the Legion of Merit after the war, and it was indeed kept secret -- to avoid offending Tito's Yugoslavia.

Mind you most of these pilots were saved even after the Allies had made the decision to abandon supporting General Draza Mihailovic's Chetniks and switch to supporting Tito's Communist Partizans in late 1943, after the Chetniks had paved the way for a German defeat in Yugoslavia.
...in Serbia and Eastern Bosnia the Serbs fought against the Germans to the end.
...Tito, the half Croat/half Slovene, took enjoyment turning his Partizan army made up of at least 80% Serbs on fellow Serbian Chetniks. He didn't give a rat's arse about the Serbian population and this was proved by the fact that Croatian Ustashe run death camps especially in Jasenovac and Stara Gradiska were liberated by the Russian Red Army despite the fact that the Partizans were in a position to do so as the Ustashe at the end of 1944 were well and truly defeated and most of their troops fled towards Austria.

It's interesting that even Stalin supported Mihailovich up until 1943, and he switched to Tito later, in 1944. But Tito and the communist owe their power in Yugoslavia mainly to the support of Churchill and the British.
...Even though the Chetnics did cooperate with the Germans and the Italians from time to time (if there wasn't for the Italians and the partisans, Serbian population in Croatia would've been completely annihilated by the Croats), but that cooperation mainly came to agreements of non-attacking, or attacking the communists.
...After Tito completely took over, and after the war ended, the communists killed in cold blood thousands and thousands of "disloyal" Serbs who weren't communists.

Considering other nations living in Yugoslavia, almost all of them collaborated with the NAZI's. The Croats even created a Nazi satellite state NDH (the Independent state of Croatia) and conducted one of the worst ever genocide against the Serbian population, almost 1 million Serbs, according to some estimations.
...The Croats and the Muslims in Bosnia, later greatly supported by western countries during the latest wars, were members of the largest SS division Hitler ever had. It was called 13th Waffen Mountain Division of the SS Handschar (1st Croatian).
Quote:
The 13th Waffen Mountain Division of the SS Handschar (1st Croatian) was one of the thirty-eight divisions fielded as part of the Waffen-SS during World War II. It was the largest of the SS divisions, with 21,065 men at its peak[citation needed], composed almost entirely of non-German Muslim and Catholic recruits drawn from Bosnia. Handschar (Bosnian/Croatian: Handžar) was the local word for the Turkish scimitar (Arabic: Khanjar خنجر), a historical symbol of Bosnia and Islam. An image of the Handschar adorned the division's flag and coat of arms.

After the war, he (Mihajlovic) was tried and convicted of high treason by Yugoslav authorities, and was consequently executed by firing squad.
...However, Mihailović decided against active resistance, allegedly because of Serb losses in World War I, in which the Kingdom of Serbia lost a quarter of its male population to the war.[2] Instead, Mihailović gathered men and weapons in the easily defensible Serbian mountains, waiting for an Allied landing in the Balkans, upon which he could attack any Germans or Italians from behind. Mihailović discouraged sabotage due to German reprisals (such as more than 3,000 killed in Kraljevo and Kragujevac) unless some great gain could be accomplished; instead, he favored delayed sabotage that could not easily be traced.

And so on...