Investigating the origins of language and culture is quite a challenge due to miniscule amount of evidence that is available. In fact in the latter part of the 19th century the royal linguistic society of London banned debate on the origin of language for fear that it was unscientific. Furthermore all contemporary languages and cultures are so entwined that they offer no evidence as to which preceded the other. However I feel that by looking cases where language has been developed in extreme conditions, it is possible to conclude that language is the precursor to culture.
There are two points that should be noted. For either language or culture to evolve there needs to be a community. As Frederick II, Emperor of Germany unfortunately demonstrated when he raised dozens of children in absolute solitude whilst trying to discover 'god's language'. The children never spoke and ultimately died without any human interaction. However, given the right conditions, human vocal organs, breathing apparatus, auditory systems and brains are so specialized for language, that the ability to acquire, and perhaps create it is a predisposition.
The overwhelming majority of mankind learns language within the context of an existing culture; however this is not necessarily the case for all. In 1997 Goldin-Meadow and Feldman studied four congenitally deaf children when they were about 18 months old. Quite obviously they were not exposed to verbal language, also their parents had no experience of sign language and so they had no experience of this either. Despite this the four children did develop their own sign language that comprised of signs for individual objects and two sign phrases/sentences. Although this study is not conclusive evidence that language predates culture, it is a good demonstration that humans are capable of developing a rudimentary language when exposure to a pre-existing culture is at an absolute minimum.
As previously stated humans appear to be predisposed with an ability to acquire and perhaps create language. However this ability is restricted, there is a time limit for the complexity of language that is adopted. There are a few studies that show that if a language is not fully learned by adolescents then the brains ability to acquire it is lost. A notable example is of a girl named Genie (Curtis 1977) who when discovered at the age of 14 had spent her life tied to a chair, nobody had ever spoken to her and if she made a sound she was severely punished. When Psychologists tried to teach her language she could grasp words, but was unable to construct full sentences. This may serve as a good example that without culture complex language cannot develop.
Although there can be no absolutely conclusive evidence that language predates culture I at least hope to have demonstrated that a group of humans could have created a rudimentary language that provided the frame work for a culture. However without this cultural framework complex forms of language such as our own are not possible.