with the help of the CIA.

https://en.wikipedia.org/wiki/1973_Chilean_coup_d%27%C3%A9tat

Although the CIA was definitely OK with what happened and helped it along, there's a little more to it than that. A sizable fraction of Chileans (not a majority) favored the coup.

Allende was no babe in the woods about this. He knew there was a high probability of a military coup, so he made the general staff retire and promoted a younger officer he thought he could trust. That is, Pinochet.

Because although he deeply believed in his and the working class's desire for equality and socialism, he knew that he was being elected into an explosive situation. The military that had ruled Chile through the 40's and 50's, before giving way to the Christian Democrats (who were exploitative career neo-liberals) were massively ingrained in the power structure of governance, to which the people of Chile resented. The military itself was actually quite weak, but over-represented by Generals who had gotten used to being the establishment and supplemented their poor pay, through corruption.

At a time when Chilean Labor unions were growing in strength, vocal and militant, and a further left Communist party contingent was equally impatient, Allende made the fatal mistake of appeasing the generals by improving their pay, and trying to draw them into his circle to avoid a civil war. They played along, but they had no intention of handing over the reigns of power to the working class.