The Crab pulsar has striking radio emission properties, with the two dominant pulse components-the main pulse and the interpulse-consisting entirely of giant pulses. The emission is scattered in both the Crab Nebula and the interstellar medium, causing multipath propagation and thus scintillation. We study the scintillation of the Crab's giant pulses using phased Westerbork Synthesis Radio Telescope data at 1668 MHz. We find that giant pulse spectra correlate at only ~2%, much lower than the one-third correlation expected from a randomized signal imparted with the same impulse response function. In addition, we find that the main pulse and the interpulse appear to scintillate differently; the 2D cross-correlation of scintillation between the interpulse and main pulse has a lower amplitude and is wider in time and frequency delay than the 2D autocorrelation of the main pulses. These lines of evidence suggest that the giant pulse emission regions are extended, and that the main pulse and interpulse arise in physically distinct regions that are resolved by the scattering screen. Assuming the scattering takes place in the nebular filaments, the emission regions are of order a light-cylinder radius, as projected on the sky. With further very long baseline interferometry and multifrequency data, it may be possible to measure the distance to the scattering screens, the size of giant pulse emission regions, and the physical separation between the pulse components.