As Erik Burigo points out in his answer, there is no rule that denies it. There is also no rule to confirm it. There is simply too little information.
Argument from Formulation
The primary objection relies upon the idea that, if it is specifically mentioned what you can do with an ability, this simultaneously reveals what you cannot. However;
Let X be the ability to place objects inside the Chest.
Let Y be the ability to place creatures inside the Chest.
X OR Y
This is not a valid formulation. You can conclude nothing about the truth of Y from the truth of X. (Don't worry, logic fans, I'll get to exclusive OR in a little bit, as the problem with using it now is that it assumes the answer before you begin.) If there is a possibility of X and a possibility of Y, and the two are not negations of each other, the truth of one does not negate the truth of the other.
The most you can say is that either Y or NOT-Y; that is, either creatures are allowed or they are not, and there is no further information to qualify this.
This brings me on to the next point.
Argument from Intention
It could be argued that I should have used an exclusive OR in the first section; that is, Objects can be put in the chest OR creatures can be put in the chest, but not both, so if objects then NOT creatures. The basis for this argument appears to be the intentions of the creator - if they had thought creatures should be allowed in the chest, then they would have said so; they did not, therefore they are not allowed. This argument cuts both ways, however, as it can also be said that had they thought creatures should NOT be allowed, they equally could have said 'Living creatures may not be placed in the chest'. This point is similar to that which CatLord raised, but cannot be used to support allowing creatures to be transported - Nothing further can be concluded about the intentions from the text as written, which brings me on to the final point.
Argument from Consistency
If omission of an option is taken to mean that option is forbidden, consistency demands we apply the same reasoning to the entire ritual.
The ritual says you can 'summon the chest to wherever you are' and that you can 'remove or add objects when it is present.', in that order. It does NOT say you can add or remove objects before the chest is summoned, or when both you and it are at the storage location. Therefore, for the sake of consistency, you cannot. This clearly violates the purpose of the chest as a method for transporting things from a dungeon without having to travel back yourself.
An objection could be that the word 'present' makes it clear that the rule refers to any time the chest is at the same location you are. However, the fact it follows directly from the line about summoning it to your presence, and directly before the line referring to dismissing it, strongly implies that it is this summoned presence that is being referred to.
This last is an obviously weak argument, but it does raise the concern that the standard objection, as raised by myself and supported by Ravn, may not be any stronger.
In summary, there is simply no absolute ruling one way or the other.
Incidently, a further objection to my view may be raised from the rules regarding the targeting of creatures and objects with powers. While objects may be targeted by powers that specify creatures at the DM's discretion, there is no equivalent reversal. However, rituals are not powers, and do not follow the same rules as powers do in most situations.