We report on the observation of a strain-induced insulator state in ferromagnetic La_0.7Sr_0.3CoO_3 films. Tensile strain above 1% is found to enhance the resistivity by several orders of magnitude. Reversible strain of 0.15% applied using a piezoelectric substrate triggers huge resistance modulations, including a change by a factor of 10 in the paramagnetic regime at 300 K. However, below the ferromagnetic ordering temperature, the magnetization data indicate weak dependence on strain for the spin state of the Co ions. We interpret the changes observed in the transport properties in terms of a strain-induced splitting of the Co e_g levels and reduced double exchange, combined with a percolation-type conduction in an electronic cluster state.