The oxidation of hydrogen is the classic example of an 'isothermal', branched-chain reaction, and it is studied here from experimental and theoretical standpoints as the natural prototype of branched-chain reactions in open systems. With an inflow of reactants and a matching outflow of products, ignition now occurs as a repetitive, oscillatory sequence of events. By identifying the critical conditions as the marginal loss of stability of the stationary-state reaction, a simple criterion for ignition can be derived. This criterion is seen to be a generalization of the elementary treatments, going over to the classical results for closed vessels in the limit of zero flow-rate; it illustrates the stabilizing effect of opening the system. The experimental location of the $p-T_a$, limit for an equimolar $H_2 + O_2$ mixture in a continuous-flow, stirred-tank reactor (c.s.t.r.) reported here, shows good agreement with the new predictions (from a simple isothermal kinetic model). Extensive measurements of extents of reactant consumption and of the (small) degree of self-heating are also presented. These lead to rates of reaction and rates of heat release. We show how these are related under conditions of steady-state (non-explosive) reaction and, hence, how accurate measurements of the small temperature-excess can be used to give measurements of the reaction rate.