We have used the Zurich Imaging Stokes Polarimeter (ZIMPOL I) with the McMath-Pierce 1.5 m main telescope on Kitt Peak to obtain linear polarization measurements of the off-limb chromosphere with a sensitivity better than 1×10$^-5$. We found that the off-disk observations require a combination of good seeing (to show the emission lines) and a clean heliostat (to avoid contamination by scattered light from the Sun’s disk). When these conditions were met, we obtained the following principal results:1. Sometimes self-reversed emission lines of neutral and singly ionized metals showed linear polarization caused by the transverse Zeeman effect or by instrumental cross talk from the longitudinal Zeeman effect in chromospheric magnetic fields. Otherwise, these lines tended to depolarize the scattered continuum radiation by amounts that ranged up to 0.2%.2. Lines previously known to show scattering polarization just inside the limb (such as the Na I łambda5889 D2 and the He I łambda5876 D3 lines) showed even more polarization above the Sun’s limb, with values approaching 0.7%.3. The O I triplet at łambda7772, łambda7774, and łambda7775 showed a range of polarizations. The łambda7775 line, whose maximum intrinsic polarizability, P$_max$, is less than 1%, revealed mainly Zeeman contributions from chromospheric magnetic fields. However, the more sensitive łambda7772 (P$_max$=19%) and łambda7774 (P$_max$=29%) lines had relatively strong scattering polarizations of approximately 0.3% in addition to their Zeeman polarizations. At times of good seeing, the polarization spectra resolve into fine structures that seem to be chromospheric spicules.