I have a 89 accord and when i go to start it has issues. It will try to turn over but not start up and just die but after a couple tries it will start and sometimes it will start and start to do a chugging thing and then die and if i try to give it a little gas to keep it idling it will die. Once it has started up and is running if i turn it off again and start it up there are no problems only after it sits for part of the day or overnight.

 

Sounds like it could possibly be the 'main relay' which is a common problem with old Honda's.