FOBs Melissa and Bill Cox write in, “What is This?”
Hi Melissa and Bill,
You have a Tomato Hornworm, which is a a hawk moth member of the family Sphingidae. They have a voracious appetite and will completely defoliate your plant, including stems and immature fruit. Tomato Hornworms are fond of many members of the family Solanaceae, which includes moonflower, morning glory, pepper, eggplant, tobacco, and potato.
The caterpillar is probably ruining your plant but if you wanted to see it go through its life cycle, you could place the caterpillar in a terrarium and feed it the foliage of the plant that you found it munching on. Alternatively, the easiest way to kill the caterpillar is to drop it in a dish of soapy water.
Tomato Hornworm covered with Beneficial Cocoons of the Braconid Wasps
Thanks Jennifer for the comment (see below).

