CHICAGO (AP) _ Hope springs eternal within a Chicago Cubs fan's breast. Only to them can spring come in January and Wrigley Field be a fitting place to spread the ashes of relatives.

''We're all a little nuts, I guess,'' said Estelle Raines, one of 1,500 nationwide devotees who began gathering Friday at the second annual Die-Hard Cubs Fan Convention to mingle with their heroes, bid on Cubs memorabilia and trade stories.

''There's just nobody else like a Cub fan, and we've run into them all over the world. You mention you're a Cub fan and you can meet people anywhere,'' said Mrs. Raines, 64, of Watervliet, Mich., as she checked into a downtown hotel with her husband, Ray.

About 2,000 Cubs fans from 31 states, including Alaska and Hawaii, made last year's convention a roaring success.

Already confirmed for return engagements are:

- Lori Washburn, 42, of Minneapolis, whose mother's ashes were spread over Wrigley Field in accordance with her wishes.

- Mrs. G. Glass Hatch, 75, whose Wrigley Field moniker, ''The Duchess,'' stems from the all-white outfit and chef's hat she has worn to games on and off since 1930.

- Comedian Tom Driesen, director of the Die-Hards.

''I missed last year because I was sick, but after I heard about it, I was determined to get here if I had to rent a helicopter to do it,'' said Benny Hahn of Neenah, Wis. ''This stuff gets in your blood. When I met my wife, that's the first thing I asked her.''

''He didn't have to,'' said Hahn's wife, Bernice. ''If he wasn't a Cub fan, I wouldn't have considered going out with him in the first place.''

Among the players who will be on hand are second baseman Ryne Sandberg, shortstop Shawon Dunston, pitcher Rick Sutcliffe and outfielders Gary Matthews and Keith Moreland.

Also attending will be Cubs General Manager Dallas Green, sure to get an earful of advice on how to improve the club. WGN-TV broadcaster Harry Caray will serve as master of cermonies for some of the functions.

Most Cubs devotees say their esprit de corps stems from being sport's most long-suffering fans. Before winning the National League East title in 1984, the Cubs' last appearance in postseason play was the 1945 World Series.

And the only thing the Cubs accomplished by winning the East Division two seasons ago was to reinforce the image of lovable losers. They took a quick 2-0 lead in their best-of-five series against the West Division-winning San Diego Padres for the NL pennant, then promptly dropped the next three games.

''Looking around, I almost feel bad about being here,'' said Aaron Buckles, a 21-year-old sophomore at Ohio State University. ''I didn't get hooked until the last game of the 1984 season. A lot of the people here have been living and dying with this club a whole lot longer than I have.''