Chi is actually air, and meridians are actually blood vessels (the charts which show meridians which have nothing to do with blood vessels are another western addition). The Chinese knew about the circulation of the blood 2000 years ago.
Modern research has demonstrated that neurovascular nodes (acupuncture points) contain a high concentration of sensory fibers, fine blood vessels, fine lymphatic vessels, and mast cells. These nodes are distributed along longitudinal pathways of the body where the collateral blood vessels supply the capillaries and fine vessels. The corneum stratum of the skin in these areas is slightly thinner with a lower electrical resistance. They also contain more sensory nerves, and have more fine vessels with sequestered mast cells than non nodes.
Ancient Chinese physicians recognized that neurovascular nodes (acupuncture points) on the surface of the body could reflect disease conditions in the internal organs, and that these same nodes could be stimulated to relieve pain and treat internal organ problems.
From the comments:
After the book [The Dao of Chinese Medicine] was published, Kendall was invited to China to give a presentation on the mistranslations of Soulie de Morant at the Shanghai medical school. After the presentation, at the tea party hosted in Kendall’s honor, some old, renowned Chinese physicians approached Kendall. They thanked him for his presentation, and told him that they were already aware of the mistranslations and their implications. Kendall asked them why they hadn’t told us in the west. Their reply was, “If westerners are naive enough to think that acupuncture works by moving magic energy in imaginary meridians, then what can we do for you?” (Robert Doane, 2010).
There's an extensive discussion of possible placebo effects in the comments.
Link thanks to Seth Roberts