The first measurements of the transferred polarization for the exclusive e⃗ p→e′K+Λ⃗ reaction have been performed at Jefferson Laboratory using the CLAS spectrometer. A 2.567 GeV beam was used to measure the hyperon polarization over Q2 from 0.3 to 1.5   (GeV/c)2, W from 1.6 to 2.15 GeV, and over the full K+ center-of-mass angular range. Comparison with predictions of hadrodynamic models indicates strong sensitivity to the underlying resonance contributions. A nonrelativistic quark-model interpretation of our data suggests that the ss¯ quark pair is produced with spins predominantly antialigned. Implications for the validity of the most widely used quark-pair creation operator are discussed.