Originally, it is Chris' plan to tell his older brother Theo about the limping person he sees entering the Westing house. But when the time comes in Chapter three, we see that he tries and does not succeed:
Chris Theodorakis was too excited to stutter out the news to his brother. One arm shot out and twisted up over his head. Dumb arm. (14)
Don't forget that Chris suffers from an unidentified crippling disease, in which he often stutters and/or loses control of his movements. His older brother is one of the few characters who is able to calm him down, speak to him like he's normal, and get him to smile. In this scene, Theo ends up telling Chris a made-up ghost story about the Westing house. Chris enjoys the attention and the story, and decides it is better than the real (and more boring story) of the person with the limp.
This is what we know.
Now, we can also make an inference that later, when the Westing will is read, Chris decides to keep the detail of the limper to himself because he believes it might be a clue to the Westing mystery, and therefore gives him an advantage others do not have.