In a large bowl, toss the shrimp with ½ cup of the chimichurri until evenly coated.
Heat a medium skillet set over medium-high heat. Add the shrimp and cook, undisturbed, until just pink on the bottom, about 1½ minutes. Flip and cook, stirring occasionally, until pink, opaque, and cooked through, about 1½ minutes more.
Serve the shrimp over the polenta and spoon the remaining ½ cup of chimichurri over top (or serve on the side).
