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Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations since teleparallel Lagrangian is built just from first derivatives of the vielbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially at FRW universe; moreover, it provides a natural inationary stage without resorting to an infaton field. The Born-Infeld parameter lambda bounds the dynamics of Hubble parameter H(t) and establishes a maximum attainable spacetime curvature.