The conformational behavior of a single, intrinsically flexible, weakly charged polyelectrolyte chain in poor solvent is analyzed by extensive computer simulations combining Monte Carlo and molecular dynamics techniques. After determining the Theta point for the charge-free case, Re focus on the weak screening Limit, corresponding to low salt concentration in the solution. We study the dependence on both the solvent strength, characterized by the relative deviation from the Theta point, tau, and the fraction of charged monomers in the chain, which is effectively tuned by varying the Coulomb interaction parameter. The conformations are discussed in terms of global properties (such as the end-to-end distance, the inertia tensor components, etc.) and functions revealing more detailed information, such as the density distribution around the center of mass and the structure factor. For chains in the Theta regime our data confirm the picture of a string of electrostatic blobs. For poorer solvents (up to tau = 0.4) we observe, upon increasing the intrachain Coulomb repulsion, a splitting of the spherical globule into a dumbbell-type structure, accompanied by a sharp increase in the chain＇s gyration radius. For sufficiently large tau, a further splitting is observed as well. Such a "necklace globule" (a sequence of transitions) had been predicted by Dobrynin, Rubinstein and Obukhov (Macromolecules 1996, 39, 2974), with a nontrivial scaling of the gyration radius with chain length and interaction parameters, which is confirmed by our data. By means of a scaling analysis, we argue that the transitions can be interpreted as thermodynamic first-order phase transformations, when taking the appropriate thermodynamic limit, which implies a scaling of the electrostatic coupling with inverse chain length.