  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 $z \simeq 6.3$ the strength of this signal, which is
proportional to the H {\sc i} fraction, has a brightness temperature $\simeq 20
  \mu K$ for a fully neutral medium. The fine structure line from this redshift
is observable at $\nu \simeq 1 \rm GHz$ 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 $\simeq 100 \mu K$; 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.
