Yes young poke weed plants can pop up anywhere.Great for magenta dye.Some like it for its medicinal properties.It must be prepared by an experienced herbalists because it potent even in small amounts & is very poisonous.Can be boiled & rinsed a few times and eaten like greens.Tasty when plants are young like yours in the pictures.Not recommended that the leaves be eaten after the plant gets tall & the stalk turns red.

Thanks for the help parityanimal and metrosideros. What threw us off was that they were growing in the exact spots where we planted pepper seeds. Perhaps the seed packs had some weeds in them.

Yes, looks like Phytolacca americana, American Pokeweed. http://en.wikipedia.org/wiki/Phytolacca_americana

If it’s not your pepper plant then I’d say it’s a pokeweed…