  We write down couplings of the fields on a single BPS Dp-brane with
noncommutative world-volume coordinates to the RR-forms in type II theories, in
a manifestly background independent way. This generalises the usual
Chern-Simons action for a commutative Dp-brane. We show that the noncommutative
Chern-Simons terms can be mapped to Myers terms on a collection of infinitely
many D-instantons. We also propose Chern-Simons couplings for unstable non-BPS
branes, and show that condensation of noncommutative tachyons on these branes
leads to the correct Myers terms on the decay products.
