Step 1: The watery, rice-water stools of cholera result from an enterotoxin secreted by Vibrio cholerae. We need to identify the mobile genetic element encoding this toxin.
Step 2: The structural genes ctxAB are part of the genome of a lysogenic filamentous phage termed CTXphi. When this phage infects a non-toxigenic vibrio, it confers the ability to make toxin, a classic example of lysogenic conversion.
Step 3: Going through the distractors: the phage genome does insert into the chromosome, yet the toxin trait originates from the phage, so attributing it simply to the chromosome misses the point. Neither extrachromosomal plasmids nor jumping transposon sequences carry the cholera toxin genes.
Step 4: So toxin production is acquired through a phage.
\[\boxed{\text{Phage (CTX phage)}}\]