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\textbf{Abstract}: The time delays between point-like images in gravitational lens systems can be used to measure both cosmological parameters as well as (sub-)structure within the lens galaxy. With the upcoming \emph{Large Synoptic Survey Telescope} (LSST), of order 1000 lens systems consisting of a foreground elliptical galaxy multiply-imaging a background quasar will become available. In an effort to assess the present capabilities of the community to measure accurately the time delays in these strong gravitational lens systems, and to provide input to future LSST cosmology feasibility studies, we pose a ``Time Delay Challenge'' (TDC). {\bf  The challenge is organised as a set of ``ladders,'' containing a group of simulated datasets to be analyzed blindly by participating independent analysis teams. Each rung on the ladder consists of a set of realistic mock observed lensed quasar light curves, increasing in complexity and realism as a result of 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, whose true time delays will be available on demand as the teams set up their analysis pipelines, and make measurements accurate enough to qualify for participation in TDC1. TDC1 consists of several thousand lightcurves, to provide the statistical power required to make meaningful statements about accuracy in the LSST era. In this paper we describe the simulated datasets in general terms; the results for TDC1 from the participating teams will be presented in a forthcoming paper. {\bf }{\bf  (GGD: perhaps the opening and closing dates of the challenge should be listed in the abstract...)}