Here's my code on SLES v11.

#! /usr/bin/ksh

MQSILIST=$(mqsilist)
RUNNING="BIP1284I: Broker 'BRK1E' on queue manager 'BRK1QME' is running. BIP8071I: Successful command completion."

echo $MQSILIST
if ["$MQSILIST" == "$RUNNING"]; then
echo "Running."
fi

Here's the error I receive.
user@host:~/scripts> ./check_BRK1E.sh
BIP1284I: Broker 'BRK1E' on queue manager 'BRK1QME' is running. BIP8071I: Successful command completion.
./check_BRK1E.sh[8]: [BIP1284I: Broker 'BRK1E' on queue manager 'BRK1QME' is running.
BIP8071I: Successful command completion.: not found [No such file or directory]

Any suggestions?

Try adding spaces. [ is a command that takes ] as its last argument, not syntactic sugar.