Divide the coconut milk into roughly equal portions of coconut cream and thin coconut milk (this can be easily done by chilling the coconut milk ahead of time and scooping out the congealed coconut cream; if the congealed mass isn't exactly half the total, pad with liquid or stop scooping, as required to even the portions).
Slice the green peppers into thin rings.
Add the diced chicken, cook until tender.
Remove the chicken and galangal with a slotted spoon; continue cooking the coconut cream mixture until the oil begins to separate.
Add the green curry paste, cook until it becomes fragrant (stirring constantly).
Return the chicken to the pan and stir. Add the remaining coconut milk, stir, add the bamboo shoots and green peppers. Heat until the chicken is fully cooked.
Serve over steamed rice.
Galangal is like ginger, only it's different. It's also known as "Siamese Ginger", Laos (the Indonesian and Thai name), and Ka.
Prepared curry pastes can be obtained from an oriental grocery store, or you can make them yourself.
I frequently consult The Original Thai Cookbook by Jennifer Brennan, and Thai Home-Cooking from Kamolmal's Kitchen by William Crawford and Kamolmal Pootaraksa.