We propose a method to study the epoch of reionization based on the possible
observation of 2p--2s fine structure lines from the neutral hydrogen outside
the cosmological H {\sc ii} regions enveloping QSOs and other ionizing sources
in the reionization era. We show that for parameters typical of luminous
sources observed at z≃6.3 the strength of this signal, which is
proportional to the H {\sc i} fraction, has a brightness temperature ≃20μK for a fully neutral medium. The fine structure line from this redshift
is observable at ν≃1GHz and we discuss prospects for the
detection with several operational and future radio telescopes. We also compute
the characteristics of this signal from the epoch of recombination: the peak
brightness is expected to be ≃100μK; this signal appears in the
frequency range 5-10 MHz. The signal from the recombination era is nearly
impossible to detect owing to the extreme brightness of the Galactic emission
at these frequencies.Comment: 17 pages, 1 figure, to appear in Ap