Yes, you can use the -blocknotify feature of multichain. This feature was introduced in bitcoin and is documented here (search for blocknotify)
https://en.bitcoin.it/wiki/Running_Bitcoin
You can configure blocknotify in the config file, so in multichain.conf you add something like this:
blocknotify=/home/simon/bin/blocknotify.sh %s
When a new block is mined, multichaind will run the blocknotify.sh script with the blockhash as an argument, replacing the %s placeholder.
A sample blocknotify.sh script might look like this:
#!/bin/sh
echo "new block: $@" >>/var/tmp/blocknotify.log
If you examine /var/tmp/blocknotify.log you should see something like:
new block: 0000fdfd653de77679c8ce3232c63fc9ca267af889f8671c779f00ff2fa7de2d
new block: 0000e774d6d7acb271d396dd7e2cdc898eda4eaff326178e4040856de9a3eb4f
new block: 0000e2437ec65725c7c49be6cbe0b180279a705b405f111c66897e919345c418