LIMIT is used to specify the number of rows returned, so isn't really appropriate here as far as i know. I would suggest something like:
Then select the row using the random number generated:
$randnumber = rand(1,NUMBER);
SELECT * from TABLE WHERE RowID = '$randnumber'
RowID should be some sort of auto incremented field using to identify rows. The 'NUMBER' above should be changed to the total number of rows in your table to avoid creating a random number which is more than your number of rows.