As usual, a very common problem. Your ABS module has gone out. I don't
think it can be repaired, only replaced. If I remember correctly, it costs
about $600 to fix at the dealer.
In the meantime, unplug the ABS fuse under the hood. Keep in mind though
that this disables ABS altogether.
That really sucks.
| I put my 99 Silverado Z71 in reverse this morning to back out of my
| and heard a buzzing noise, like the sound you here when your ABS brakes
| actuating. I looked at the dash and my ABS light was on. I mashed the
| brakes a few times hoping it was just something sticking and would break
| loose but it didn't. I parked it and shut it off and the noise still
| remained. I got underneath it and saw a small motor on the driverside,
| inside the frame rail, that was running. I tapped it a few times with a
| wrench and it still wouldn't stop. I ended up unplugging the battery.
| ideas what I might be looking at? Anyone had this problem before?