There have been some significant NASA events' commemorations recently going back to the start of the American Space Age. And among the great and brave men and women being noted there is a lack of the note of America's first astronaut, well, not a man or a woman but a monkey, a chimpanzee, named Ham, to be more correct.
January 31, 1961(yes, 52 years ago), Ham was launched in a Mercury capsule on a suborbital flight that preceded and prepared for the subsequent launch of Alan Shepard in his suborbital flight of May 5, 1961 and the start of American manned space flight (not withstanding those of the X-15).
The Iranians have now claimed to do something similar, put a monkey into space. Of course, clearly, the Iranian monkey volunteer was not named "Ham".
Ham died, January 19, 1983, almost 13 years after his ride into history.
As to whether another chimp like Ham would be the subjected to his experience, is doubtful. As a part of what happened to Ham and how he was used, the use of animals as experimental subjects for science has been severely changed. Today, most of the research done on chimps and monkeys has been reduced and almost eliminated as a part of ethical treatment and the law.
Now, the only use US of animals in space and particularly ham, can be seen in episodes of "Pigs In Space".