The Chain Devil's Animate Chains action allows it to animate chains near to it and use them as weapons:
Animate Chains (Recharges after a Short or Long Rest). Up to four chains the devil can see within 60 feet of it magically sprout razor-edged barbs and animate under the devil's control, provided that the chains aren't being worn or carried.
Each animated chain is an object with AC 20, 20 hit points, resistance to piercing damage, and immunity to psychic and thunder damage. When the devil uses multiattack on its turn, it can use each animated chain to make one additional chain attack. An animated chain can grapple one creature of its own but can't make attacks while grappling. An animated chain reverts to its inanimate state if reduced to 0 hit points or if the devil is incapacitated or dies.
The feature gives the statistics for these animated chains, but does not specify any speed.
Does this mean these animated chains have a speed of 0 and can thus only attack things near them?
Best Answer
The chains have no speed
Abilities do only what they say they do
In 5e, spells and abilities do only what they say they do. If the ability gave the chains a speed, it would have said so in the line detailing the chains' statistics.
Not only does the ability not give the chains a speed, but the chains are also explicitly defined as objects. An object does not have a speed unless an effect of ability explicitly gives one to it.
Compare to animate objects
For example, compare the wording of this ability to the spell animate objects:
Notice even an intelligent construct, a creature, (which the chains are not) is required to specifically have a speed given to them.
The ability is lacking much more information than just the numerical speed
Not only does the ability not list a speed but it also lacks a description of how the chain would move (crawling? flying?) and how they would decide where to go. Remember, these chains do not have any form of intelligence or any kind of sight. So, how could the chains have the capability to even decide where to move?
Also note that the Chain Devil is not granted the ability to command the chains to do anything except attack and grapple (which aren't even commands so much as automatic things that happen under the listed conditions). Even if the Chain Devil tried to command them, the chains have no ears or any capacity to understand speech.
The chains are simply objects that are able to make attacks and grapple when the Chain Devil meets the listed conditions. There is no reason to assume that the intent was to give them a speed and, in fact, the lack of key information needed for this to be possible is a decent indicator that this was not the intent. Thus, the chains have no speed.
Note: Having no speed and having 0 speed are mechanically different. Something with no speed cannot move unless something gives it a speed. Something with 0 speed could move once the 0 speed condition is alleviated or if they are able to get a bonus to speed that would increase it above 0. (thanks @DavidCoffron)