One could potentially suggest observations of atomic locations partly with chaos theory by suggesting that the seemingly random pattern simply results from a sufficiently small Lyapunov time that allows nearby trajectories to diverge very quickly, making randomness and chaotic trajectories indistinguishable.
However, the inverse of Lyapunov time should not be faster enough such that trajectories diverge faster than the speed of light, but this is very difficult to assess with individual particles that are either entangled or which cannot have simultaneous position and momentum determined.
In the observational constraints and in seeing the simpler explanation of deterministic chaos, why can't quantum randomness potentially be explained by chaotic motion? It seems physicists already possess the capability to predict the exact future state of single particles at a time at least.