We report experimental observations of chemical turbulence and line defects in a three-dimensional (3-D) Belousov-Zhabotinsky (BZ) reaction-diffusion system. Transitions from spiral waves to 3-D chemical turbulence to line defects are observed. These transitions are caused by concentration gradients across the third dimension in the 3-D reaction medium, indicating the observed line defects have a 3-D structure. The line defects come out of the 3-D turbulent state, and become smooth with the increase of the control parameter. Simulation with the two-variable Oregonator model in the 3-D system reproduces similar line defects.