Terahertz (THz) imaging can see through otherwise opaque materials. However, because of the long wavelengths of THz radiation (lambda = 400 mu m at 0.75 THz), far-field THz imaging techniques suffer from low resolution compared to visible wavelengths. We demonstrate noninvasive, near-field THz imaging with subwavelength resolution. We project a time-varying, intense (>100 mu J/cm(2)) optical pattern onto a silicon wafer, which spatially modulates the transmission of synchronous pulse of THz radiation. An unknown object is placed on the hidden side of the silicon, and the far-field THz transmission corresponding to each mask is recorded by a single-element detector. Knowledge of the patterns and of the corresponding detector signal are combined to give an image of the object. Using this technique, we image a printed circuit board on the underside of a 115-mu m-thick silicon wafer with similar to 100-mu m (lambda/4) resolution. With subwavelength resolution and the inherent sensitivity to local conductivity, it is possible to detect fissures in the circuitry wiring of a few micrometers in size. THz imaging systems of this type will have other uses too, where noninvasive measurement or imaging of concealed structures is necessary, such as in semiconductor manufacturing or in ex vivo bioimaging.