A multi-component fiber that includes a core component surrounded by a distinct sheath component is provided. The core component is formed primarily from polylactic acid and the sheath component is formed primarily from a polymeric toughening additive. The sheath/core configuration may provide a variety of different benefits to the resulting fiber. For instance, the polymeric toughening additive can help increase the ability of the fiber to absorb energy that arises from stresses imparted during fiber drawing, which increases the overall toughness and strength of the fibers. At the same time, the presence of the toughening additive in the sheath component can enhance the degree of bonding to other fibers (the same or different), such as when employed in a nonwoven web material. Another benefit of the present invention is that the sheath/core configuration may be formed from a thermoplastic composition in which the polylactic acid and polymeric toughening additive are blended together.