You can choose any value for X as you cast Chamber Sentry. The value chosen for X doesn't directly affect the number of +1/+1 counters Chamber Sentry enters the battlefield with, but it does let you pay more mana and thus spend more colors of mana to cast it.

If Chamber Sentry enters the battlefield without being cast, it receives no +1/+1 counters.

If an effect allows you to spend mana as though it were mana of any color to cast Chamber Sentry, you consider only the actual mana spent to determine how many counters it receives.

If another creature enters the battlefield as a copy of Chamber Sentry, consider what mana was spent to cast that creature to determine how many +1/+1 counters it enters with.

Colorless mana won't give Chamber Sentry another +1/+1 counter. Colorless is not a color.

The value of X chosen when you activate Chamber Sentry's first activated ability doesn't have to be the same value of X that you chose when you cast it.