I have been having a sluggish omnibox, and one of the fixes people suggest is to delete the history provider cache file from the user directory, however I was not able to find this file on Chrome OS, if anyone knows where it is, I would appreciate knowing where I could delete it.
When I originally answered this I did it through my phone and had to hand type the path as I was trying to remove all sorts of malware from a friends Win7 PC.
I suspect that this is different on different platforms and you did not specify yours.
If you are on Windows I would try using CCleaner as it would make mady other recommendations. This post shows a likely path
Did not find on MacOs, but this answer may be of help
CCleaner will list and remove '.../Chrome/user data/default' is where I found it