  Let $X$ denote a compact set which is laminated by Riemann surfaces. We
assume that $X$ carries a positive CR line bundle $ L\rightarrow X$. The main
result of the paper is that there exists a positive integer $s$ so that if $v$
is any continuous $(0,1)$ form with coefficients in $L^{\otimes s}$ there
exists a continuous section $u$ of $L^{\otimes s}$ solving the equation
$\bar\partial_b u=v$.
