A chemical reactor clamp for supporting a glassware or equivalent chemical reactor having a neck includes: (a) a central housing; (b) a spring-biased yoke connected to the central housing and extending outwardly therefrom for a attachment to the reactor neck; (c) a female socket on the central housing and adapted to receive a clamp rod; and, (d) a clamp rod locking mechanism on the central housing at the female socket. There is also a combination of the clamp with the rod, as well as a system with the clamp, rod and rod support unit, as well as a system with these components and a second rod (vertical rod) and a vertical rod base, to provide multiple degrees of freedom of movement for the clamp.