  We introduce the poset NC^d_n of all noncrossing partitions such that each
block has cardinality 1 modulo d and each block of the dual partition also has
cardinality 1 modulo d. We obtain the cardinality, the M\"obius function, the
rank numbers, the antipode, and the number of maximal chains. Generalizing work
of Stanley, we give an edge labeling such that the labels of the maximal chains
are exactly the d-parking functions. We also introduce two classes of labeled
trees: the first class is in bijective correspondence with the noncrossing
partitions in NC^d_n and the second class is in bijective correspondence with
the maximal chains.
