The positron decay of 38Ca has been investigated using the 36Ar(3He,n) reaction with an enriched 36Ar gas target. A delayed 1568-keV γ ray with a half-life of 0.47+/-0.02 sec is attributed to a positron branch to the 1695-keV level of 38K. Upper limits of 3% or better were found for transitions to other low-lying levels. Using the measured half-life and the decay energies, the branching ratio to the 1695-keV level is calculated from β-decay systematics to be (21+/-4)%. The ft for this transition (3.41+/-0.09) establishes Jπ=1+ for the 1695-keV level. An additional result was the observation of an allowed transition from 38K to the 3936-keV level of 38Ar.