  Precision measurements of the acoustic peaks of the cosmic microwave
background indicate that neutrinos must be freely streaming at the photon
decoupling epoch when T ~ 0.3 eV. This requirement implies restrictive limits
on ``secret neutrino interactions,'' notably on neutrino Yukawa couplings with
hypothetical low-mass (pseudo)scalars \phi. For diagonal couplings in the
neutrino mass basis we find g < 1 x 10^-7, comparable to limits from supernova
1987A. For the off-diagonal couplings and assuming hierarchical neutrino masses
we find g < 1 x 10^-11 (0.05 eV/m)^2 where m is the heavier mass of a given
neutrino pair connected by g. This stringent limit excludes that the flavor
content of high-energy neutrinos from cosmic-ray sources is modified by \nu ->
\nu' + \phi decays on their way to Earth.
