Does compression on a TrueCrypt drive compromise the security?

I choose “Compress drive to save disc space” under drive properties.

The compression should have no effect on the security offered by TrueCrypt.

If the compression is applied before the encryption, i.e. at the filesystem level hosted within an encrypted file/partition then the data will still be as well encrypted as it would be uncompressed. No one would know it was compressed data until they'd managed to decrypt some of it anyway.

If the compression is applied after the encryption then it will have little or no effect either on security or space used - in fact it would most likely back-fire and result in wasting space - so you'll just be wasting CPU cycles. Data encrypted with cryptographically safe algorithms should not have enough redundancy for the compression algorithm to find.

Usual implementation is to set compression on the filesystem which is within the TrueCrypt container. For example if you are running NTFS filesystem, then you can use the NTFS compression tools. This will make a difference to the size of data within the TrueCrypt volume, so you can fit more data in it. It obviously will not change the size of the volume itself, but you can always do that manually.