Step 1: Understand what an omphalocele is.
An omphalocele (exomphalos) is a midline ventral wall defect at the umbilicus in which abdominal viscera herniate into the base of the umbilical cord. The defining feature is that the herniated gut is enclosed within a translucent membranous sac $-$ it is NOT exposed (this is what separates it from gastroschisis).
Step 2: Recall the embryology of the sac wall.
The omphalocele represents a failure of the physiological midgut herniation to return into the abdomen by week 10-12. Because the viscera stay within the umbilical cord, their covering is built from the layers of the cord itself. From outside in, this sac is composed of amnion (outer), Wharton's jelly, and peritoneum (inner).
Step 3: Identify the outer covering asked for.
The outermost, visible covering of the omphalocele sac is the amnion, the extra-embryonic membrane that lines the umbilical cord. Hence the sac's covering is derived from the amnion.
Step 4: Reject the distractors.
$\bullet$ Chorion forms the fetal part of the placenta, not the cord covering.
$\bullet$ Mesoderm contributes to body-wall muscle/connective tissue, not the sac's outer layer.
$\bullet$ Endoderm forms the gut lining itself, not the protective covering of the herniated organs.
Step 5: Conclusion.
Since the omphalocele sac is the persisting covering of the umbilical cord, its outer layer is the amnion.
Final answer: Option 1 - Amnion.