I have a new hampton bay ceiling fan with a remote and pull chains. In the middle of the night the fan will change speeds or the light may suddenly come on. Is this a problem with the remote?

Change the frequency. Your neighbor may be using the same freq. Just change the dip switches to match in the remote and receiver in the canopy.

KISS is correct.

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php)

I have a new hampton bay ceiling fan with a remote and pull chains. In the middle of the night the fan will change speeds or the light may suddenly come on. Is this a problem with the remote?
I have also heard that the radio frequencies of overhead aircraft can change the direction/speed of a fan and also turn the light on and off as well. My Hunter fan does this as well.

Possible, but less likely than another RF product in the neighborhood. Either way, changing the frequency should fix it.