Parallel Coordinates are a popular data visualization technique for multivariate data. Dating back to as early as 1880 PC are nearly as old as John Snow's famous cholera outbreak map of 1855, which is frequently regarded as a historic landmark for modern data visualization. Numerous extensions have been proposed to address integrity, scalability and readability. We make a new case to employ PC on conditional data, where additional dimensions are only unfolded if certain criteria are met in an observation. Compared to standard PC which operate on a flat set of dimensions the ontology of our input to Conditional Parallel Coordinates is of hierarchical nature. We therefore briefly review related work around hierarchical PC using aggregation or nesting techniques. Our contribution is a visualization to seamlessly adapt PC for conditional data under preservation of intuitive interaction patterns to select or highlight polylines. We conclude with intuitions on how to operate CPC on two data sets: an AutoML hyperparameter search log, and session results from a conversational agent.