B. Wayne Hughes' Greeley's Galaxy worked a mile at Churchill Downs Thursday, displaying his readiness for the Kentucky Derby (gr. I), according to 83-year-old veteran California trainer Warren Stute.After leaving the starting gate under exercise rider Mikki Fincher, Greeley's Galaxy began the work at the eighth pole and went a mile in 1:40 3/5."It was a little fast," said Stute, who declared his colt fit after the work. "He's in good enough shape, if he gets beat it won't be because he's not fit."Under the care of Stute's son Glen, the chestnut son of Mr. Greeley vanned to Churchill Downs over the weekend from Chicago's Arlington Park. Before the work, Stute said his shipper came "just perfect."He's a nice, big colt with a good temperament, he travels well and he's got a lot of sense about him," Stute said.Before the workout just after the 8:30 maintenance, Stute said he was hoping for "a slow mile, and then maybe sneak in an extra quarter."Stute said the colt would work again three or four days before the Derby, and Kent Desormeaux was booked to ride Greeley's Galaxy on race day.Owner Hughes was happy with the performance and on hand at Al Stall's Barn 47 where Stute is setting up shop."He worked very nicely," said Hughes. "He had a good, hard gallop out. Warren's from the old school, and he has his own way of doing things. At this point we just hope we'll get in."Because Greeley's Galaxy was not nominated to the Visa Triple Crown Challenge during the early or late nomination periods, he will have to be supplemented to the Derby at a cost of $200,000.If 20 or more horses are entered in the Derby, preference will be given to horses that were Triple Crown nominees to the exclusion of Greeley's Galaxy.After breaking his maiden in his second career start, Greeley's Galaxy won an allowance race at Santa Anita before shipping to the Midwest to take the Illinois Derby (gr. II) by 9 1/2 lengths as the favorite.