We present a scheme for laser cooling applicable for an extremely dilute sample of magnetically trapped antihydrogen atoms($bar{H}$). Exploiting and controlling the dynamical coupling between the $bar{H}$s motional degrees of freedom in a magnetic tr
ap, three-dimensional cooling can be achieved from Doppler cooling on one dimension using the $1s_{1/2}-2p_{3/2}$ transition. The lack of three-dimensional access to the trapped $bar{H}$ and the nearly separable nature of the trapping potential leads to difficulties in cooling. Using realistic models for the spatial variation of the magnetic fields, we find that it should be possible to cool the $bar{H}$s to $sim 20$ mK even with these constraints.
