I would use two MAX7219's for that, one to control the 60 LEDs, the other to drive the 4 time digits (HH:MM).
Run the LEDs in no-decode mode so you can individually control the 8 bits in the 8 registers to turn on (add) one LED after another:
0b00000001, 0b00000011, 0b00000111, 0b00001111, etc.
Run the other in regular decode mode to have it display the digits for you.
Good idea. That gets it down to two chips. He still has to buy something though.
Here's my guide to the MAX7219:http://www.gammon.com.au/forum/?id=11516
I got 10 x MAX7219 from eBay for $4.50 so you can probably afford that. Try searching for "10PCS IC MAXIM DIP-24 MAX7219CNG".