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Time-lapse live cell imaging is a powerful tool for studying signaling network dynamics and complexity and is uniquely suited to single cell studies of response dynamics, noise, and heritable differences. Although conventional imaging formats have the temporal and spatial resolution needed for such studies, they do not provide the simultaneous advantages of cell tracking, experimental throughput, and precise chemical control. This is particularly problematic for system-level studies using non-adherent model organisms such as yeast, where the motion of cells complicates tracking and where large-scale analysis under a variety of genetic and chemical perturbations is desired. We present here a high-throughput microfluidic imaging system capable of tracking single cells over multiple generations in 128 simultaneous experiments with programmable and precise chemical control. High-resolution imaging and robust cell tracking are achieved through immobilization of yeast cells using a combination of mechanical clamping and polymerization in an agarose gel. The channel and valve architecture of our device allows for the formation of a matrix of 128 integrated agarose gel pads, each allowing for an independent imaging experiment with fully programmable medium exchange via diffusion. We demonstrate our system in the combinatorial and quantitative analysis of the yeast pheromone signaling response across 8 genotypes and 16 conditions, and show that lineage-dependent effects contribute to observed variability at stimulation conditions near the critical threshold for cellular decision making.