Chemotaxis in Caenorhabditis elegans depends critically on the rate of change of attractant concentration computed as the worm moves through its environment. This computation depends, in turn, on the neuron class ASE, a left-right pair of pair of chemosensory neurons that is functionally asymmetric such that the left neuron is an on-cell, whereas the right neuron is an off-cell. To determine whether this coding strategy is a general feature of chemosensation in C. elegans, we imaged calcium responses in all chemosensory neurons known or in a position to contribute to chemotaxis to tastants in this organism. This survey revealed one new class of on-cells (ADF) and one new class of off-cells (ASH). Thus, the ASE class is unique in having both an on-cell and an off-cell. We also found that the newly characterized on-cells and off-cells promote runs and turns, respectively, mirroring the pattern reported previously for ASEL and ASER. Our results suggest that the C. elegans chemotaxis network is specialized for the temporal differentiation of chemosensory inputs, as required for chemotaxis.