We present new sensitive CO(2-1) observations of the 30 Doradus region in the Large Magellanic Cloud. We identify a chain of three newly discovered molecular clouds that we name KN1, KN2, and KN3 lying within 2-14 pc in projection from the young massive cluster R136 in 30 Doradus. Excited H2 2.12 μm emission is spatially coincident with the molecular clouds, but ionized Brγ emission is not. We interpret these observations as the tails of pillar-like structures whose ionized heads are pointing toward R136. Based on infrared photometry, we identify a new generation of stars forming within this structure.