Two-dimensional (2D) atomic crystals, such as graphene and transition-metal dichalcogenides, have emerged as a new class of materials with remarkable physical properties(1). In contrast to graphene, monolayer MoS2 is a non-centrosymmetric material with a direct energy gap(2,5). Strong photoluminescence(2,3) a current on/off ratio exceeding 10(8) in field-effect transistors(6), and efficient valley and spin control by optical helicity(7-9) have recently been demonstrated in this material. Here we report the spectroscopic identification in a monolayer MoS2 field-effect transistor of tightly bound negative trions, a quasiparticle composed of two electrons and a hole. These quasiparticles, which can be optically created with valley and spin polarized holes, have no analogue in conventional semiconductors. They also possess a large binding energy (similar to 20 meV), rendering them significant even at room temperature. Our results open up possibilities both for fundamental studies of many-body interactions and for optoelectronic and valleytronic applications in 2D atomic crystals.