  The absolute differential cross sections for small-angle proton elastic
scattering off the nuclei $^{12,14-17}$C have been measured in inverse
kinematics at energies near 700 MeV/u at GSI Darmstadt. The hydrogen-filled
ionization chamber IKAR served simultaneously as a gas target and a detector
for the recoil protons. The projectile scattering angles were measured with
multi-wire tracking detectors. The radial nuclear matter density distributions
and the root-mean-square nuclear matter radii were deduced from the measured
cross sections using the Glauber multiple-scattering theory. A possible neutron
halo structure in $^{15}$C, $^{16}$C and $^{17}$C is discussed. The obtained
data show evidence for a halo structure in the $^{15}$C nucleus.
