Design a Hashtable

I was asked this question in an Interview and was left stumped, even though i came up with an answer I didn't feel comfortable with my solution. I wanted to see how experts here feel about this question.

I am exactly quoting the question as it came out of the Interviewer. "Design a Hash-table, You can use any data-structure you can want. I would like to see how you implement the O(1) look up time". Finally he said It's more like simulating a Hash-table via another Data-structure.

Can anyone light me with more information on this question. Thanks!

PS: Main reason for me putting this question is to know how an expert designer would start off with the Design for this problem && one more thing I cleared the interview somehow based on the other questions that were asked but this question was in my mind and I wanted to find out the answer!