According to the book "What If?", he had a very good chance at it in 1945. The best chance at it, according to that book, would have been to beat the Communists back into Manchuria, which becomes a Chinese North Korea, with Mao almost entirely subservient to Stalin.
I think you are remembering wrong. It wasn't Chiang beating the Communists so bad that they fled into Manchuria. It was Chiang abandoning any attempt to take Manchuria after the Soviet withdrawl because the Nationalists were defeated very badly there. Instead, Chiang would drive them out south of the Great Wall, but abandon everything north of it.
Instead of attempting to defeat the Communists militarily, Chiang would enact his government and economic reforms which would eliminate most of the corruption that was the downfall of the Nationalists.
But, if I remeber right, I thought Chiang secretly hated the US. He only accepted thier help because he thought he had no other choice? Well, thats what Wikapedia tells me anyway.
Chiang didn't hate the US, but he had a very difficult relationship with several specific Americans. He also felt very let down by them at various times after World War II.
Chiang was above all a Chinese patriot, and he would cooperate with anyone who could help China. He certainly looked to the US for help because the US did not have any colonial ambitions in China unlike the Europeans or Soviets. And his in-laws had a lot of ties to the US.
In general, it is possible for the Nationalists to defeat the Communists after 1945, but it requires many different actions by Chiang. Chiang staked everything on his ability to defeat the Communists militarily first, and then he would take the necessary reforms and eliminate any remaining regional warlords. Chiang bet wrong. The failure to reform the army hampered his ability to defeat the Communists militarily. The failure to reform the economy meant much of the public welcomed the arrival of the Communists. The failure to reform the government meant alienating members of the US government and media which was providing him support.
Chiang should have realized that he was not facing the small, isolated group of "bandits" he meant to eliminate entirely at Xi'an in 1936. Instead, in 1945 he was facing a much larger group of dedicated individuals who benefited from the respectability of "fighting" alongside the Nationalists against the Japanese, and who were well supplied from the supplies they received from surrendered Japanese and left by the Red Army. They were not going to be quickly eliminated, and he needed to take measures to ensure that the Nationalists were strong enough for the long haul. Chiang fundamentally misjudged the situation.
It would be very hard for Chiang to make a sudden decapitating attack that would have killed Mao and all other members of the Communist leadership in 1945. Chiang did in fact take the old Communist "capital" at Yenan, but at that time Mao and the others had plenty more places to go to. It is perhaps possible for Chiang to do that in 1936 if he somehow learns of the plan to kidnap him by General Zhang Xueliang. Chiang defeats the attempt, arrests Zhang Xueliang, and is able to eliminate the Communists right before the Marco Polo Bridge Incident begins the war with Japan. Whether he could eliminate the Communists is debateable, but it is at least feasible.