This is completely possible. There are two options
1. keep the server as vanilla and use lots of command block trickery
2. use a bukkit/spigot server and install some kind of skyblock plugin.
Google will help you in terms of using a bukkit server. Just google "creating a spigot server" and then im sure youll be able to figure out how to fiddle with plugins.
In terms of the command block method, this is how I thought of doing it in my head.
a. Summon an invisible, small, invincible, noGravity armorstand where each chest should be.
b. /setblock each chest in the correct place so the armourstand is the same block space as the chest.
c. use command blocks so that when a button is pressed a hopper in placed 1 block above the armourstands. After a length of time the hopper is set to air
(/execute @a[type=Armor_stand] ~ ~ ~ setblock ~ ~1 ~ hopper)
d. use several randomisers (
http://minecraft.gamepedia.com/Miscellaneous_circuits#Random_number_generator) and use the differing comparator outputs to power different command blocks.
e. Each command block will /summon a different item 2 blocks above each Armourstand. Use this tool to get /summon commands with NBT data, custom names and all the rest
https://mcstacker.bimbimma.com/. The items will spawn above the hopper, which will place the items into the chest. After the time delay, the hoppers will be set to air.
That should be it. Google is your friend on this one.
