My ´88 Elite XL has the same problem. It is nearly impossible to get it started. If it does start, the engine just sputters; if I accelerate the engine, it dies. After an extended time of idling, the engine will suddenly begin running normally.
I took it in to a Honda dealer this week and they told me today they have it fixed. I believe they put in a new choke, but I´m not sure since I haven´t yet picked it up.