May you choose *not* to use the free construction chain?
As correctly stated by @unor, you may opt not to use the chain building, but normally pay for resources (English Rules, p. 4):


  If the player has built the structure named there during a previous Age, that player can build the structure for free, meaning without having to fulfill the resource cost.


Both French and German rules confirm the above. The German rules are even more elaborate, as they state (German Rules, p. 4):


  Wenn der Spieler, der das Gebäude errichten möchte, auch das auf der Karte erwähnte andere Gebäude aus dem vorangegangenen Zeitalter in seiner Stadt besitzt, muss er die Kosten nicht bezahlen, sondern kann das Gebäude kostenfrei bauen.
  
  (English) When the player, who wants to construct a building, has also other buildings from a previous Age mentioned on the card that already exist in his city, he does not have to pay the cost, since he may construct the building free of charge. 


If it was obligatory, the German rules would state darf er die Kosten nicht bezahlen, i.e., must not pay the cost.



It should be noted, however, that when you're playing the "Free City" 2-player variant, the Free City has to use chain building, if the chosen card benefits from one (English Rules, p. 7).


  If the card chosen for the Free city can benefit from a free construction (chain), this free construction MUST be performed.


The existence of this rule in the 2-player variant merely confirms that during the normal game (3-8 players) you may either choose the chain or build normally.

Also note that, if you're playing a Team game, you are not allowed to purchase resources from your teammate, if you can build a structure through chain (English "City" Rules, p. 10).


  It is forbidden for the teammates to :
  
  
  share coins,
  trade cards,
  not pay for commerce between them,
  buy resources from each other while they can build a structure through a chain.
  




Note that you are not able to buy resources that you can already produce, but only the resources you're missing (English Rules, p. 4).


  Often, a player will want to build a structure requiring resources he or
  she does not produce. If these resources are produced by a neighboring city – players sitting directly to the left or right of that player – the player will be able to purchase the missing resource(s) through commerce.


This is also confirmed by the "City" expansion rules (English "City" Rules, p. 10).


  A player must use their own resource before buying one from their neighbors.