Two-dimensional (2D) transition metal dichalcogenides (TMDs), with their atomic thicknesses, high carrier mobility, fast charge transfer, and intrinsic spin-valley couplings, have been demonstrated one of the most appealing candidates for next-generation electronic and optoelectronic devices. The synthesis of TMDs with well-controlled crystallinity, quality and composition is essential to fully realize their promising applications. Similar to that in III-V semiconductor synthesis, the precise precursor supply is a precondition for controllable growth of TMDs. Although great efforts have been devoted to modulate the transition metal supply, few effective methods of chalcogen feeding control were developed. Herein we report a strategy of using active chalcogen monomer supply to grow TMDs and their alloys in a robust and controllable manner. It is found that at a high temperature, the active chalcogen monomers (such as S, Se, Te atoms or their mixtures) can be controllably released from metal chalcogenides and, thus, enable the synthesis of TMDs (MX2, M = Mo, W; X = S, Se, Te) with very high quality, e.g., MoS2 monolayers exhibit photoluminescent circular helicity of ~92%, comparable to the best exfoliated single-crystal flakes and close to the theoretical limit of unity. More intriguingly, a uniform quaternary TMD alloy with three different anions, i.e., MoS2(1-x-y)Se2xTe2y, was accomplished for the first time. Our mechanism study revealed that the active chalcogen monomers can bind and diffuse freely on a TMD surface, which enables the effective nucleation and reaction, quick chalcogen vacancy healing, and alloy formation during the growth. The chalcogen monomer supply strategy offers more degrees of freedom for the controllable synthesis of 2D compounds and their alloys, which will greatly benefit the development of high-end devices with desired 2D materials.