Thankfully, CHB has the answer for you. Option 1: Leave it on the curb. Sanitation tells us that they will pick up trees, without lights or ornaments, from the curb and will take them to Staten Island for chipping and mulching there. They will do this between January 5th and the 11th.
Option 2: Mulchfest! Take your tree to Fort Greene Park this weekend (Saturday and Sunday, from 10am-2pm) for a huge chipping session where there will be refreshments for all provided by Provisions (YUM), located on Fulton Street. Bring the kids and dogs for a good, end-of-holiday-season get-together. And, best of all, the mulch will be used right there in our own Fort Greene Park to protect and nourish our trees and shrubs.
Option 3: Bring your used Christmas tree to the Hollenback Community Garden on Washington Avenue between Gates & Greene (also Saturday and Sunday) so that the Parks Department can haul them all over to Fort Greene Park for chipping and distribution to the needy trees and shrubs in the park. A great alternative for those who don't live near the park (or have a huge-ass tree that they don't want to haul as far).
If you want to keep it local, and provide much needed mulch for our own Fort Greene Park, take the trees to either Fort Greene Park or the Hollenback Garden this weekend. It is a little more exercise and you have to hang onto that dead tree for a little while longer, but keeping it local and helping the park are good.