This short note by the late G. Kempf, which was originally going to be published in 1993, unfortunately got lost and is now recovered. The author constructs, over an algebraically closed field of characteristic zero, a three-dimensional Jacobian \(X\) whose theta divisor \(\theta\) contains an elliptic curve. The construction starts from two isogenies \(\psi_E: E'\to E\) and \(\psi_F: F'\to F\) of degree two (\(E\) being an elliptic curve and \(F\) a three-dimensional p.p.a.v., respectively), and \(X\) is constructed as the quotient of \(E'\otimes F'\) after the image of a Klein 4-group given by 2-torsion elements. Then it is proved that \(\theta\) contains a translate of \(\text{im}~E'\).