If you mean a direct opposition or test:
* Defy: To refuse to obey or submit to.
* Confront: To face or deal with a difficult or unpleasant situation.
* Dispute: To argue or disagree with something.
* Question: To express doubt about something.
* Contest: To compete with someone or something.
If you mean something that is difficult to achieve:
* Obstacle: Something that blocks progress or makes it difficult to move forward.
* Hurdles: Difficulties or problems that must be overcome.
* Task: A piece of work that must be done.
* Problem: A situation that needs to be solved.
If you mean an invitation to compete:
* Dare: To invite or provoke someone to do something dangerous or risky.
* Provocation: Something that causes anger or a reaction.
To get a more precise synonym, please provide the sentence or context in which you want to use the word "challenge."