mysql> select * from Transactions ORDER BY RAND() LIMIT 1;

+-------+-----------------+--------+-----------+------+-------+----------+----------+------+---------+---------------------+
| id    | EffectiveTicket | Ticket | TimeTaken | Type | Field | OldValue | NewValue | Data | Creator | Created             |
+-------+-----------------+--------+-----------+------+-------+----------+----------+------+---------+---------------------+
| 94058 |               0 |  10094 |         0 | Set  | Queue | 6        | 3        | NULL |    1328 | 2005-02-03 11:40:41 |
+-------+-----------------+--------+-----------+------+-------+----------+----------+------+---------+---------------------+
1 row in set (3 min 5.23 sec)

mysql> 
mysql> explain select * from Transactions ORDER BY RAND() LIMIT 1;
+--------------+------+---------------+------+---------+------+--------+---------------------------------+
| table        | type | possible_keys | key  | key_len | ref  | rows   | Extra                           |
+--------------+------+---------------+------+---------+------+--------+---------------------------------+
| Transactions | ALL  | NULL          | NULL |    NULL | NULL | 270299 | Using temporary; Using filesort |
+--------------+------+---------------+------+---------+------+--------+---------------------------------+
1 row in set (0.00 sec)