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Two-dimensional (2D) transition metal trichalcogenides (TMT) have recently been extensively studied due to their intriguing electronic and magnetic properties. Here, based on first-principles calculations, we predict a new 2D TMT material MnSiTe₃, which possesses both ferromagnetism and half-metallicity. The cleavage energy of the bulk MnSiTe₃ is found to be very low, suggesting its monolayer counterpart can be obtained via direct mechanical exfoliation. More intriguingly, we demonstrate that both the ferromagnetism and half-metallicity are preserved when reducing the dimensions from the bulk to monolayer. For the monolayer MnSiTe₃, we calculate the strengths of exchange interactions between nearest, next-nearest and next-next-nearest neighbors of Mn ions. The long-range ferromagnetic order is further confirmed by Monte Carlo simulations within the Heisenberg model, and the Curie temperature T_c is shown to be ~70K. Apart from the exchange interactions between magnetic atoms, the Ruderman-Kittel-Kasuya-Yosida interaction mediated by itinerant carriers also plays a crucial role in determining the ferromagnetic ground state. These findings provide a new 2D material for exploring applications in nano spintronics.