  We study a one-dimensional Brownian motion conditioned on a self-repelling
behaviour. Given a nondecreasing positive function f(t), consider the measures
mu_t obtained by conditioning a Brownian path so that L_s< f(s), for all s<t,
where L_s is the local time spent at the origin by time s. It is shown that the
measures mu_t are tight, and that any weak limit of mu_t as t tends to infinity
is transient provided that t^{-3/2}f(t) is integrable. We conjecture that this
condition is sharp and present a number of open problems.
