LASCO captures piece of itself
Since the launch of SOHO in December 1995, images similar to this one have been observed about a dozen times. As in each previous case, it appears that some of SOHO's multi-layer thermal insulation (MLI), which has become brittle after over nine years' exposure to solar radiation, has flaked off and is passing in front of the wide-angle view of the coronagraph.
The streaking in this 19 second exposure is similar to what you would capture if you were to hold a camera lens open for several seconds and take a picture of snow falling. Just as the snowflakes that passed closest to the lens would appear as fat, out of focus streaks, this MLI flake also appears as a thick, bright streak.
What caused the MLI to flake off? Probably, a micrometeorite struck the brittle insulation, not an uncommon event for spacecraft. This type of image has sometimes been observed when a cover of one of the instruments has closed with some force and knocked off some of the spacecraft's insulation, but no covers were closing on this occasion.