Technically yes, though the way you describe the idea is fundamentally incoherent. The OS inherently controls all software running in the context of that OS, and this is unavoidable.
The thing that exists instead is the ability to, using dedicated hardware, run certain extremely-high-trust programs outside of the OS entirely. This is part of the premise of devices like hardware security modules (HSMs), though also many processors have what is often called a "secure enclave". It is possible to write software for such a "secure execution environment", sign it (so that the HSM/enclave will accept it and also so that the OS can't tamper with it without breaking the signature), and load it into the secure hardware. The secure hardware then executes it completely independently of the OS and the main CPU/RAM/etc. that the OS and all of its software runs on, or at least isolated from that hardware (though physically different hardware is better than even hardware-mediated isolation on shared RAM, etc. due to risk of side-channel attacks and other vulnerabilities).
Note that you still need trusted execution somewhere, to create the signed image for the trusted execution hardware. Also, while the OS can't tamper with the signed image, it could in theory either refuse to load it, or replace it wholesale with a different signed image. The only way you can actually do this reliably is if the program is already loaded into the trusted environment before the untrusted OS is introduced.