Many motile microorganisms are able to detect chemical gradients in their surroundings to bias their motion toward more favorable conditions. In this study, we observe the swimming patterns of Caulobacter crescentus, a uniflagellated bacterium, in a linear oxygen gradient produced by a three-channel microfluidic device. Using low-magnification dark-field microscopy, individual cells are tracked over a large field of view and their positions within the oxygen gradient are recorded over time. Motor switching events are identified so that swimming trajectories are deconstructed into a series of forward and backward swimming runs. Using these data, we show that C. crescentus displays aerotactic behavior by extending the average duration of forward swimming runs while moving up an oxygen gradient, resulting in directed motility toward oxygen sources. Additionally, the motor switching response is sensitive both to the steepness of the gradient experienced and to background oxygen levels, exhibiting a logarithmic response.