  Polyatomic molecules have rich structural features that make them uniquely
suited to applications in quantum information science, quantum simulation,
ultracold chemistry, and searches for physics beyond the Standard Model.
However, a key challenge is fully controlling both the internal quantum state
and the motional degrees of freedom of the molecules. Here, we demonstrate the
creation of an optical tweezer array of individual polyatomic molecules, CaOH,
with quantum control of their internal quantum state. The complex quantum
structure of CaOH results in a non-trivial dependence of the molecules'
behavior on the tweezer light wavelength. We control this interaction and
directly and nondestructively image individual molecules in the tweezer array
with >90% fidelity. The molecules are manipulated at the single internal
quantum state level, thus demonstrating coherent state control in a tweezer
array. The platform demonstrated here will enable a variety of experiments
using individual polyatomic molecules with arbitrary spatial arrangement.
