In this Letter we describe a novel method for tunable viscoelastic focusing of particles flowing in a microchannel. It is proposed that some elasticity, inherently present in dilute polymer solutions, may be responsible for highly nonuniform spatial distribution of flowing particles across the channel cross section, yielding their "focusing" in the midplane of the channel. A theory based on scaling arguments is presented to explain the lateral migration and is found to be in a very good agreement with the experimental observations. It was found that, in agreement with the theoretical prediction, the particles would have different spatial distribution depending on their size and rheology of the suspending medium. We demonstrate how the viscoelastic focusing can be precisely controlled by proper rheological design of the carrier solution.