Chalice is expensive and less useful, yes. But it is the best value you're getting for your money as far as I know. Even though Zilean has the really nice ability to charge Tear somewhat quickly and at low mana cost to him (if you max W Second, which I do. But this is personal preference.) it still takes too much time to work well enough for you.
Yeah, chalice is far from optimal, but the time investment into Tear is WAY too high for it to ever be viable in most games, as your money doesn't even have good returns for a long time, and then you're missing important power spikes//opportunities. The reason I don't go chalice is you never have enough money.
It is easy to get caught up in the 'Bombs Kill People!" part of Zilean and think that's all he does. But IMO, that's only about half of it.
Bombs do kill people, and you are very good at that early game, especially with 650 auto range. But, only one of your spells does damage(Rewind doubles it, but even so, mages have at least 2 spells that do damage and an ultimate that does.)
Because of this, after early game it becomes very difficult to do large amounts of meaningful damage, especially when you consider you'll probably have to E yourself and maybe your enemy in order to not get blown up.
Along with the fact that you're not getting a ton of AP on a support budget, you've gotta focus on the other amazing parts of zileans kit past early game. 30 second cooldown ultimates, and your e.
This is why I max W second (after two points in E) because I think any points past the second in E are largely wasted, the skill lasts basically forever at that point anyway. I get max CDR as early as possible. (Glyphs + 1 Quint gives 10%. 5% in masteries + Ionian Boots of Lucidity.) I Take CDR boots, although it wastes the CDR on Frost Queen's Claim (which you get eventually), because you need 40% CDR as early as possible to get 30 second cooldown ults, which is Zilean's biggest strength in mid-late game.
After that, I just build damage // utility (because aura items are very good investments as support) which is honestly quite standard.
So, my build is something like...
Start: Spellthief's Edge 3 Pots. > Sightstone (or Frostfang if can't afford) then Frostfang (or vice-versa). > Boots 1, Chalice, Upgrade Boots > Choice.
Choice just means that from here I decide based on the game, but in general I'll be doing something like (Although maybe not in this exact order...) > Finish Frost Queen's Claim > Banner of Command > Twin Shadows // Frozen Heart // Mikaels' // Whatever the team needs.
You DEFINITELY don't want Rylais BTW. You already have your E for slowing people, and slows don't stack very well. Also, it's a lot of wasted money on HP when honestly, you shouldn't get caught in the first place.