Can you use chains to chain up a creature in the middle of combat? (What if it becomes stunned or paralyzed for a round? - Would this be enough time?). What would the creatures condition be afterwards? Would it be restrained and still be able to attack?
You can bind a creature during combat, but the extent of those bindings vary with context.
As per the rules, there is no explicit rule on how to bind a creature during combat using nonmagical chains or manacles, meaning that there is nothing in the books regarding the effect of the creature's status or the necessary checks or rolls required. Therefore, this answer is based both off of my experience as a DM and as a bouncer who has had to place people in restraints before.
Applying any sort of restraint on a creature that is not already held down or immobilized is nearly impossible. Just look at police officers, who usually straddle a resisting target on the ground before applying handcuffs or leg shackles. It would thus make sense that a creature couldn't be bound unless it was first victim of a condition which reduces its speed to 0 (grappled, paralyzed, petrified, restrained, stunned or unconscious).
Furthermore, actually using an object to bind someone falls under the "Use an Object" action. You would then attempt to place preliminary restraints on the creature, which may trigger a contest if the creature can still resist or attempt to break free (which it can do unless it is paralyzed, petrified, stunned or unconscious). If the bindings are manacles or chains that click shut, then the creature is bound. In the case of using rope, you would have to make an additional check to tie the knot, aka an Intelligence (sleight of hand) check according to XGtE pg. 78, which sets the DC to break free.
On subsequent turns, you could apply additional bindings which may further restrict the creature's movement. As for the condition this would apply on the creature, it heavily depends on the type of binding used, and how the creature is bound. Preliminary bindings, such as manacles or leg shackles, could hamper the creature without outright applying a condition, and that would depend on how tight the bindings are and how the limbs are bound (a creature with both hands tied in front of them can still wield a sword, but not a sword and a shield). Full-body chains should apply the restrained condition provided that they immobilize the legs and restrict arm movements. Overall, it's a judgement call from the DM.