Amplified spontaneous emission is a common noise source in active optical systems, it is generally seen as being an incoherent process. Here we excite an ensemble of rare earth ion dopants in a solid with a π pulse, resulting in amplified spontaneous emission. The application of a second π pulse leads to a coherent echo of the amplified spontaneous emission that is correlated in both amplitude and phase. For small optical thicknesses, we see evidence that the amplified spontaneous emission and its echo are entangled.