C. elegans worms exhibit a natural chemotaxis towards food cues. This provides a potential platform to study the interactions between stimulus valence and innate behavioral preferences. Here we perform a comprehensive set of choice assays to measure worms' relative preference towards various attractants. Surprisingly, we find that when facing a combination of choices, worms' preferences do not always follow value-based hierarchy. In fact, the innate chemotaxis behavior in worms robustly violates key rationality paradigms of transitivity, independence of irrelevant alternatives and regularity. These violations arise due to asymmetric modulatory effects between the presented options. Functional analysis of the entire chemosensory system at a single-neuron resolution, coupled with analyses of mutants, defective in individual neurons, reveals that these asymmetric effects originate in specific sensory neurons.