It depends on whether you think "fun" is an adjective.
Researching the word “funnest” and its close relation “funner” turned out to be a lot less fun than I had hoped. The opinions are so varied that I became completely engrossed and frustrated and forgot to call my mother on her birthday. Sorry, Mom.
‘Fun,’ the Noun
First, the easy part. Everyone agrees that “fun” was originally just a noun. For example, you could say, “We had fun,” which is the grammatical equivalent of “We had cake.” Fun is more of an abstract thing than cake, but they're both nouns. People at the same party may disagree about whether they had fun, whereas they would probably all agree that they had cake, but “fun” and “cake” are both nouns.
‘Fun,’ the Adjective
But now we head down the slippery slope of fun because many modern sources grudgingly (2) accept that “fun” can also be used as an adjective, as in “Squiggly throws a fun party.” (1, 3) In that sentence “fun” is an adjective that modifies the noun “party.” It was a fun party.
How "fun" made its way from a noun to an adjective is a great illustration of how language can change over time. Nouns can be used to modify other nouns, and when they are they're called attributive nouns. In the phrase "sugar cookie," "sugar" is a noun, but it's being used in an attributive way to describe the cookie. Attributive nouns do the same thing as adjectives. You could say, "I ate a sugar cookie" or "I ate a yummy cookie." The sentences are constructed the same way, but "sugar" is an attributive noun and "yummy" is an adjective.
The Oxford English Dictionary notes a few uses of "fun" as an attributive noun such as "fun fair" and "fun-fest" in the early 1900s. It was probably from there that "fun" worked its way from noun to adjective. In English, nouns often end up becoming adjectives too. (1, 2)
A few sources note that using "fun" as an adjective is a generational thing. It's much more acceptable to children, (3) youngsters, (4) slackers, (5) and people who were born after 1970. (6) A Google Ngram search, which shows how often words are used in the books Google has scanned, shows that writers started using “fun” as an adjective more often around 1960, and using it that way has been steadily increasing ever since.
In fact, I suspect many of you listening probably use “fun” as an adjective without even thinking about it, and it doesn't sound strange to your ears, but remember, that wasn't always the case. It's a concession on the part of language traditionalists to not freak out when you say something such as "It was a fun party." They'd prefer you say something like “We had fun at the party.”