First Chest Location Crota’s End Raid Destiny
The first chest is when you get to the Traverse the Abyss checkpoint. Run towards the first light past one of the pillars. Then turn left and follow a path into the darkness. You will get to a door behind which is the first chest in the Crota’s End Raid in The Dark Below in Destiny. This particular chest spawns in random locations so you may not see it here straight away. The other locations are similarly to the left and right of the path you should take. The door with the chest behind it has a glowing light above it.
Another possible location is at the start go to the right. Eventually you see a little balcony which is the entrance to the room where a chest may spawn. Here is a map that shows the possible locations that the chests can spawn:

First Chest Spawn Points Crota’s End Raid The Dark Below Destiny
Here is a video showing you how to get to the first chest in crota’s end raid:
Second Chest Location Crota’s End Raid Destiny
Here is a video showing you how to get to the second loot chest in Crota’s End:
Chest Contents and Chances Crota’s End Raid
Here is some information about the possible contents of the two above chests and the chances associated with getting the loot from the chests:
http://www.reddit.com/r/DestinyTheGame/comments/2ow4ze/reddit_loot_table_for_crotas_end_normal_mode/
Solo the First Chest Crota’s End Raid
Here is a video that shows how to get to the first chest on your own using a Hunter:
Solo the Second Chest Crota’s End Raid
Here is a guide that talks about how to solo different parts of the Crota’s End raid including how to get to the second chest on your own:
http://www.reddit.com/r/DestinyTheGame/comments/2pc8tj/crotas_end_solo_guide_compilation/
MORE TO COME AS MORE CHESTS ARE FOUND