According to Aaron Wilson of Scout.com, they recently tried out TE Justin Peelle.
Peelle, listed at 6'4" and 255 pounds, was originally drafted by the San Diego Chargers in the fourth round of the 2002 NFL draft. He's 32 years old and spent his first four years with the Chargers, a pair of season with the Miami Dolphins and the last three years with the Atlanta Falcons.
He's no Moeaki but he appears to be a decent receiving tight end. His best season is a 29-catch, 228 yard and two-touchdown season with the Dolphins in 2007 and he started 11 games for the Falcons in 2008 when TE Ben Hartsock went on IR.
Last Sunday's game against the Buffalo Bills saw Chiefs tight ends Leonard Pope and Jake O'Connell combine for four receptions for 39 yards. Not great but certainly not terrible by any means.
Peelle was released by the Falcons with an injury settlement so the Chiefs tryout could have been an opportunity to see where he stands physically.