The isotopic compositions of Zn together with Cr, Ti, and Ca have been measured in a number of calcium aluminum-rich inclusions (CAIs) from the Allende meteorite. The aim of this work was to test astrophysical models which predict large excesses of 66Zn to accompany excesses in the neutron-rich isotopes of Ca, Ti, Cr, and Ni. Some of the CAIs show clearly resolved but small excesses for 66Zn which are at least an order of magnitude smaller than predicted. This result may simply reflect the volatility and chemical behavior of Zn as compared to the other (more refractory) anomalous elements found in these samples. Alternatively, revision of parameters and assumptions used for the model calculations may be required. 66Zn found in the more refractory spinel-rich component of these CAIs shows no clearly resolvable difference from the silicate fraction. This indicates that the expected large 66Zn excess, if it indeed existed, has not survived even in the more refractory components of the CAIs. The corresponding Ca, Ti, and Cr data show correlated excesses on 48Ca, 50Ti, and 54Cr in proportions as typically observed in most non-FUN CAIs.