"Chalice. A constellation of a life-giving goblet appears on you. Whenever you cast a spell using a spell slot that restores hit points to a creature, you or another creature within 30 feet of you can regain hit points equal to 1d8 + your Wisdom modifier."

Can the extra heal be on the original creature if it is within 30ft?

It’s not as clear as it could be. I would say yes. In context, “another” means “other than you,” not “other than the original target.”

I also have a question about the Chalice constellation. How does it interact with Aura of Vitality? Chalice form gives an extra 1d8+wis when using a spell that consumes a spell slot. Aura of Vitality consumes a spell slot, but lasts 1 minute with concentration and gives you the ability to heal using your bonus action.

I guess the same question would apply to Aura of Life.

The wording says that the chalice ability triggers "Whenever you cast a spell using a spell slot that restores hit points to a creature," so would it only apply to the initial casting and not the continued effect of gaining a bonus action heal?

The Chalice ability only applies to the initial casting.   You cast Aura of Vitality once, therefore the Chalice effect happens once.  

To answer the original poster, yes.  If you use cure wounds on a target while chalice is up, based on the wording of chalice, you could give that same target the effect of chalice.  I feel its pretty clear.  “You or another creature within 30 feet” is basically “Who can I see within 30 feet, including myself”

Song of Blues is spot on with their interpretation, and the wording on Chalice cements this.  When you cast Aura of Vitality is when you expend the slot, and Chalice specifically states it only activates when a spell slot is expended.  

Would Supreme Healing max out the Chalice 1d8?

No, because the Chalice is not a spell.  Supreme Healing only applies to the dice that are rolled as part of a spell, while the Chalice is a separate effect that goes off in response to a spell being cast.

So if I cast healing word and have chalice up and targeting the same character, I would do 1d4 + Wisdom + 1d8 + Wisdom worth of healing to that creature?

Not precisely.  When you cast Healing Word, you would give 1d4+Wis healing to the target, then choose yourself or a creature within 30 feet of you (which could be the same target as before but doesn't have to) and give 1d8+Wis healing to them.

When do we choose who gets the second heal? After the first is done? Or do we choose our targets and roll all the dice at the same time? 

It doesn't specify, so you should be able to choose the most advantageous option.

If I were to cast healing word while in the chalice form into a ring of spell storing, would the effect persist for later use even if I am no longer in starry form

The chalice heal effect is no tied to the spell you are casting, rather the Chalice form. So you have to pick who you want to heal at the time of casting a healing spell or loose that extra healing.

Is an action required to cast starry form chalice? 

Transforming into your starry form is done as a bonus action. The benefit the chalice form provides occurs "Whenever you cast a spell using a spell slot that restores hit points to a creature," which could be an action or a bonus action.