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In this paper, multiple input multiple output (MIMO) channel estimation formulated as a chance constrained problem is investigated. The chance constraint is based on the presumption that the estimated channel can be used in an application to achieve a given performance level with a prescribed probability. The aforementioned performance level is dictated by the particular application of interest. The resulting optimization problem is known to be nonconvex in most cases. To this end, convexification is attempted by employing a Chernoff inequality. As an application, we focus on the estimation of MIMO wireless channels based on a general L-optimality type of performance measure.