  We report the discovery of a surprising binary configuration of the
double-mode Cepheid OGLE-LMC-CEP-1347 pulsating in the first (P_1=0.690d) and
second overtone (P_2=0.556d) modes. The orbital period (P_orb=59d) of the
system is five times shorter than the shortest known to date (310d) for a
binary Cepheid. The Cepheid itself is also the shortest-period one ever found
in a binary system and the first double-mode Cepheid in a spectroscopically
double-lined binary. OGLE-LMC-CEP-1347 is most probably on its first crossing
through the instability strip, as inferred from both its short period and fast
period increase, consistent with evolutionary models, and from the short
orbital period (not expected for binary Cepheids whose components have passed
through the red giant phase). Our evolutionary analysis yielded a
first-crossing Cepheid with a mass in a range of 2.9-3.4 Msun (lower than any
measured Cepheid mass), consistent with observations. The companion is a stable
star, at least two times fainter and less massive than the Cepheid (preliminary
mass ratio q=0.55), while also redder and thus at the subgiant or more advanced
evolutionary stage. To match these characteristics, the Cepheid has to be a
product of binary interaction, most likely a merger of two less massive stars,
which makes it the second known classical Cepheid of binary origin. Moreover,
further evolution of the components may lead to another binary interaction.
