This is one of those times where the lawyer’s experience with non-competes is critical. It really, really depends on a lot of specific things.

• Is the non-compete enforceable?
• Who is the competitor?
• How is your relationship with your current employer?
• Is your current employer genuinely concerned about competition or was this just a standard document they have all employees sign?
• Even if it’s a competitor, would you be working in a department that won’t concern your current employer, or with a customer base that doesn’t overlap with the customer base you are working with at your current employer?
• How has your current employer handled non-compete violations with other employees in the past?
• Does the potential employer know about the non-compete? How do they feel about it? 
• How badly does the potential employer want you?

Again, there are so many considerations. However, you want this new job. Don’t just say “no” to a great opportunity out of your general fear that your non-compete prevents you from taking the job. Talk to a board-certified employment attorney first so that you can understand how these types of  situations actually play out in practice and what options are available. There are lots of creative ways to handle it that may allow you to take advantage of that next, great opportunity, despite having signed the non-compete agreement.