When Chazal instituted to say Hallel on Yomim Tovim, Rosh Chodesh was not included. A minhag then developed to say Hallel on Rosh Chodesh as well; but in order to maintain the distinction between this Hallel and other, more technically obligatory ones, only half-Hallel is said.
Shabbos Bulletin Parshas Vaera 5779
About the Author: Lev Seltzer
Lev Seltzer has been a member of Beis Tefillah from just a short time after its founding. He currently manages the BTYA.org website, and can be found every morning in the BTYA "Vasikin Room" where he is the gabbai of the minyon.