May 12 is the new June 1 when it comes to compensatory picks in the NFL.
Previously, June 1 was the cut-off date for free agent signings to be counted into the compensatory pick formula but the NFL changed that to May 12 this year. So today's date could trigger a restart to free agency with some of the available veterans.
The reasoning behind this is likely to get those veterans into OTAs and minicamps with a team earlier so that they have a better shot at making the team. Some teams might have shied away from signing those players until after June 1 because of the compensatory pick formula.
So, the Chiefs can sign any free agent out there after today and it will NOT count against their compensatory pick formula. The Chiefs are not expected to get any high compensatory picks next year after signing WR Jeremy Maclin to a five-year contract this year. Over The Cap has the Chiefs right on the cusp of receiving a seventh round compensatory pick.
The Chiefs don't seem to be in the market for any veteran players at the moment so this may not change anything but we shall see.