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This letter explains a new, highly sensitive method for the detection of neutrons, which uses the T$_{1/2}=845$ ns delay in the decay of $^{128}$I at the 137.8 keV energy level, resulting from the capture of thermal neutrons by iodine nuclei in NaI and CsI scintillation detectors. The use of delayed coincidence techniques with a several $\mu {\rm s}$ time frame for delayed events allows for the highly effective discrimination of neutron events from any existing background signals. A comparison of ambient neutron measurements between those identified through the suggested method from a cylindrical, \o$\, 63 \, {\rm mm}\times 63\, {\rm mm}$ NaI(Tl) scintillator and those from a low-background proportional $^3$He counter experimentally demonstrates the efficacy of this neutron detection method. For an isotropic, $4\pi$, thermal neutron flux of 1 ${\rm n}\, {\rm cm}^{-2}\, {\rm s}^{-1}$, the absolute sensitivity of the NaI detector was found to be $6.5 \pm 1\, {\rm counts}\, {\rm s}^{-1}$ with a background of $0.8\, {\rm events}\, {\rm day}^{-1}$ and a delay time frame of $\Delta {\rm t}=1\, \mu $s. The proposed method can provide low-background experiments, using NaI or CsI, with measurements of the rate and stability of incoming neutron flux to a greater accuracy than 10$^{-8}\, {\rm n}\, {\rm cm}^{-2}\, {\rm s}^{-1}$., Comment: accepted for publication / NIM A