The phrase "a complex chain of" is correct and usable in written English.
It can be used to describe a series of interconnected elements or processes that are intricate or complicated in nature.
Example: "The research revealed a complex chain of events that led to the environmental disaster."
Alternatives: "a complicated series of" or "an intricate sequence of".
According to the study published in Science, cannabinoids, through a complex chain of events, rev up the dopamine system.
But behind many mortgages is a complex chain of parties that service mortgages or invest in them through an array of complicated legal agreements.
Tobacco grown in farms across the country often enters domestic and international supply chains through a complex chain of middle-men, tobacco leaf-buyers and farming co-operatives.
He was also functionally illiterate and so far as we can tell from Huang, incapable of stringing together a complex chain of thought.
When photons strike light-sensitive neurons in the eye, they kick-start a complex chain of chemical reactions and electrical impulses that travel to the brain, and culminate in an image of a particular moment in time.
Their goal was to create a narrative in which major characters appeared repeatedly, many in various contexts, lending coherence to a complex chain of events and revealing the multifaceted roles that some individuals played.
The advertisement, based on a complex chain reaction of moving parts from the Accord itself, was approved and given the working title "Cog".
In many cases the manufacturer has been assumed the root cause for these shortcomings; however, the use of commercial kits and their appropriate application in a clinical setting involves a rather complex chain of constituencies and events.
The economics of these platforms has spawned a new branch of micro, first developed by Jean Tirole and Jean Charles-Rochet in the early 2000s, (There is a good introduction by David Evans here).The big idea is that changing prices in a two-sided market triggers a more complex chain of events that the simple "price up, quantity down" of a regular firm.
Or monitoring a more complex chain of events (e.g.: a microwave door being opened and closed; cooking commencing; the door being opened and closed again; cooking continuing; and cooking ending) in order to support the ability to create smart alerts for whether an appliance is available for use, for example.
"It's a pretty complex chain of supply.
