ABSTRACT: The time delays between point-like images in gravitational lens systems can be used to measure cosmological parameters as well as probe the dark matter (sub-)structure within the lens galaxy. The number of lenses with measuring time delays is growing rapidly due to dedicated efforts. In the near future, the upcoming _Large Synoptic Survey Telescope_ (LSST), will monitor ∼10³ lens systems consisting of a foreground elliptical galaxy producing multiple images of a background quasar. In an effort to assess the present capabilities of the community to accurately measure the time delays in strong gravitational lens systems, and to provide input to dedicated monitoring campaigns and future LSST cosmology feasibility studies, we pose a “Time Delay Challenge” (TDC). The challenge is organized as a set of “ladders,” each containing a group of simulated datasets to be analyzed blindly by participating independent analysis teams. Each rung on a ladder consists of a set of realistic mock observed lensed quasar light curves, with the rungs’ datasets increasing in complexity and realism to incorporate a variety of anticipated physical and experimental effects. The initial challenge described here has two ladders, TDC0 and TDC1. TDC0 has a small number of datasets, and is designed to be used as a practice set by the participating teams as they set up their analysis pipelines. The non mondatory deadline for completion of TDC0 will be December 1 2013. The teams that perform sufficiently well on TDC0 will then be able to participate in the much more demanding TDC1. TDC1 will consists of 10³ lightcurves, a sample designed to provide the statistical power to make meaningful statements about the sub-percent accuracy that will be required to provide competitive Dark Energy constraints in the LSST era. In this paper we describe the simulated datasets in general terms, lay out the structure of the challenge and define a minimal set of metrics that will be used to quantify the goodness-of-fit, efficiency, precision, and accuracy of the algorithms. The results for TDC1 from the participating teams will be presented in a companion paper to be submitted after the closing of TDC1, with all TDC1 participants as co-authors.