The Kansas City Chiefs typically don't announce any contract agreements until the pen hits the paper and it's totally official. That's probably the reason you haven't seen the Chiefs announcing any draft picks -- many of the players aren't getting into Kansas City until today, before rookie minicamp, which starts tomorrow.
The KC Star's Adam Teicher noted the timing of it all in this blog post and also writes in a I-know-more-than-what-I'm-saying way that both seventh round picks -- Jerome Long and Junior Hemingway -- should be among the first to sign. I'd guess that the Chiefs announce a handful of signings this weekend.
With the NFL's rookie wage scale, signing draft picks has never been easier. The rookie wage scale was out last season but with the NFL lockout things were still all hurried and it didn't feel normal. Apparently, signing your draft class in May is the new normal.
All the draft picks signed in relatively quick fashion last year with the exception of Justin Houston, who was among the last picks in the NFL to sign for reasons that still aren't known today.