I assume you are referring to MySQL, the feature you want to look into straight from the docs is time stamps.
This would probably update the db table created by schema to the field type you are looking for:
MODIFY COLUMN `created` TIMESTAMP NOT NULL DEFAULT current_timestamp;
Just stumbled on this post stating timestamp support should be in for Drupal 8, so I assume (and I coud be wrong) it probably is not supported out of the box for D7. Just change the type to TIMESTAMP in your array, and see what gives but I would not wager on this working through the D7 schema api.
UPDATE:
Actually, look in the post. The patch will add support to timestamp in D7.
Major kudos to drupalshrek for sharing this with us.
Database schema, once patched would be as follow:
<?php
$schema['vchess_moves'] = array(
'description' => 'Contains the list of moves for each game',
'fields' => array(
'timestamp' => array(
'description' => 'Exact date and time of the move',
'type' => 'timestamp',
'not null' => TRUE,
?>
Go see the post above for the patch, I won't repost his stuff here, not sure if doing so would be proper.
Hope this helps, happy coding.