We argue that all the necessary ingredients for successful inflation are present in the flat directions of the Minimally Supersymmetric Standard Model. We show that out of many gauge-invariant combinations of squarks, sleptons, and Higgs bosons, there are two directions, LLe and udd, which are promising candidates for the inflaton. The model predicts more than 10(3) e-foldings, with an inflationary scale of H(inf) approximately O(1-10) GeV, provides a tilted spectrum with an amplitude of delta(H) approximately 10(-5) and a negligible tensor perturbation. The temperature of the thermalized plasma could be as low as T(rh) approximately O(1-10) TeV. Parts of the inflaton potential can be determined independently of cosmology by future particle physics experiments.