A Northwest Side man was convicted Wednesday of the crossbow murder of a homeless man who was shot through the heart with an arrow in what prosecutors deemed ''a thrill killing.''

Ted Light, 21, stood before Cook County Circuit Court Judge Earl Strayhorn, who found him guilty of the Sept. 17, 1987 murder of Gaylord Tolbert, 33, who had been sleeping on cardboard on Lower Wacker Drive when he was killed.

Throughout the three-day bench trial, Light impassively watched as former friends described how he had bragged that he had killed a homeless black man downtown with a serrated-razor-tipped arrow he had shot from a crossbow.

In his closing argument, Light`s defense attorney Gary Sternberg told Strayhorn that Light was innocent and that his bragging was just indicative of his interest in telling tall tales.

Sternberg also told Strayhorn that the key prosecution witness, who was driving the car in which Light rode when the killing occurred, was a liar concerned with saving himself from criminal prosecution.

But in their closing arguments prosecutors Anthony Calabrese and Rimas Cernius said Light`s bragging showed the unusual killing was done for thrills. Calabrese said that Light had to talk about the killing to relive the moment over and over.

Citing the testimony of witnesses, Calabrese said the bragging had begun the day after the killing, before word of it had appeared in the press.

Days later Light drove some friends to the scene and showed them the flattened cardboard that Tolbert had been lying on. The bragging continued for 18 months before a friend turned him in to police, Calabrese said.

''He`s giving details, something only someone who did the shooting would know,'' Calabrese said. ''That`s how we know it`s a thrill killing.''

During the trial, Dewight Lambert, 30, a convicted burglar, testified that he and Light were riding around with Light`s crossbow on the night of the killing, looking for something to shoot.

They spotted a stray dog, but lost it, Lambert said, and Light suggested they go downtown to look for large rats. When they found none, Light suddenly told Lambert to stop the car, then aimed the crossbow out of the window and shot it, Lambert said.

''I seen a man that was sitting up. He fell back down,'' Lambert said.

''I drove very fast.''

The next day, Light began bragging that he had killed a bum with the crossbow, friends testified. Light did not testify in his own defense, and both defense witnesses testified that they had heard Light speak of the killing.

Light`s friend ''Peter Velic knew the man had been killed with a hunting arrow . . . before the arrow was even taken out of the body,'' Calabrese said. ''The autopsy wasn`t even performed before he was talking about it.''

Bathsheba Birman, another friend, testified that she first heard Light talk ''quite convincingly'' about the killing in December 1987. She said he talked about it again in February 1989, saying that he was certain police never would link him to the killing.

She called police to see if a homeless man had been killed in the way Light described. When she learned Tolbert had, she called detectives and told them what she knew.

Lambert first was charged with murder, but the charge was dismissed for lack of evidence. Light was arrested nearly 18 months after the killing.

He is scheduled to be sentenced on July 23. He could be sentenced to 20 to 60 years in prison or more if Strayhorn considers the killing brutal and heinous.