We have used fast-ion-beam laser spectroscopy to measure the 1s2 s 3 s-1s2 p 3 P o intervals in Be iii to an absolute accuracy of 1 part in 10 8. Our results are (in cm− 1): σ (1s2 s 3 S 1-1s2 p 3 P 0 o= 28 864.6120 (4), σ (1s2 s 3 S 1− 1s2 p 3 P 1 o= 26 853.0534 (3), σ (1s2 s 3 S 1− 1s2 p 3 P 2 o)= 26 867.9484 (3). These results are an improvement over previous measurements by nearly 3 orders of magnitude and show evidence of uncalculated O (α 4 Z 4) relativistic corrections. Once those terms are computed, our measurement will allow QED calculations in two-electron atoms to be tested at the 100 ppm level.