When we moved into our house in '89 this was growing along a south facing wall. I cut it down every year and by summer it branches out at least 3 feet. The fruit is bright red, when ripe and has little seeds inside that look like pepper seeds.The flowers are small and purple. The branches also have nasty thorns on them. I hope the attached photos will help identify this plant.
Some kind of lycium, possibly lycium barbarum, "matrimony vine" Try this link from Montana, where it grows http://montana.plant-life.org/species/lyci_barba.htm Your initial thought of pepper was right, this is a relative in the nightshade family. Glen
Thank you! I should have known it was something used by Chinese herbalists. The previous owners of the house were Chinese. Maybe I'll use the berries now instead of letting the birds eat them all.