  We study the distribution of gluons in transverse space in the nucleon at
moderately small x (~10^{-2}). At large transverse distances (impact
parameters) the gluon density is generated by the 'pion cloud' of the nucleon,
and can be calculated in terms of the gluon density in the pion. We investigate
the large-distance behavior in two different approaches to chiral dynamics: i)
phenomenological soft-pion exchange, ii) the large-N_c picture of the nucleon
as a classical soliton of the pion field, which corresponds to degenerate N and
Delta states. The large-distance contributions from the 'pion cloud' cause a
\~20% increase in the overall transverse size of the nucleon if x drops
significantly below M_pi/M_N. This is in qualitative agreement with the
observed increase of the slope of the t-dependence of the J/psi photoproduction
cross section at HERA compared to fixed-target energies. We argue that the glue
in the pion cloud could be probed directly in hard electroproduction processes
accompanied by 'pion knockout', gamma^* + N -> gamma (or rho, J/psi) + pi + N',
where the transverse momentum of the emitted pion is large while that of the
outgoing nucleon is restricted to values of order M_pi.
