The microchip will travel to the asteroid, named Bennu, aboard the agency's Origins-Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) spacecraft.
The robotic mission will spend more than two years at the 1,760-foot-wide asteroid. The spacecraft will collect a sample of Bennu's surface and return it to Earth in a sample return capsule.
"We're thrilled to be able to share the OSIRIS-REx adventure with people across the Earth, to Bennu and back," said Dante Lauretta, principal investigator of the OSIRIS-REx mission from the University of Arizona in Tucson.
"It's a great opportunity for people to get engaged with the mission early and join us as we prepare for launch," Lauretta said.
Those wishing to participate in "Messages to Bennu!" should submit their name online by September 30.
"You'll be part of humankind's exploration of the solar system - How cool is that" said Bill Nye, chief executive officer of The Planetary Society, the organisation collecting and processing the entries.
The OSIRIS-REx mission goal is to address basic questions about the composition of the very early solar system, the source of organic materials and water that made life possible on Earth, and to better predict the orbits of asteroids that represent collision threats to the Earth.
It will collect a minimum of 60 grams of surface material. Once the sample return capsule deploys, the spacecraft will be placed into a long-term solar orbit around the Sun, along with the microchip and every name on it.
"It is exciting to consider the possibility that some of the people who register to send their names to Bennu could one day be a part of the team that analyses the samples from the asteroid 10 years from now," said Jason Dworkin, mission project scientist at NASA's Goddard Space Flight Center, Greenbelt.