A thermotropic liquid crystalline polymer melt polymerized in the presence of a viscosity modifier that can help increase the “low shear” viscosity of the resulting composition is provided. The increased “low shear” viscosity can minimize drooling of the polymer composition during processing and also allow it to possess a greater melt strength, which facilitates its ability to be processed in a wide variety of applications without losing its physical integrity. Despite having a relatively high “low shear” viscosity, the present inventors have discovered that the viscosity modifier does not substantially increase the “high shear” melt viscosity of the polymer composition. In this regard, the ratio of the “low shear” viscosity to the melt viscosity is generally very high, such as within a range of from about 50 to about 1000.