Array or List in Java. Which is faster ?

The Java way is that you should consider what data abstraction most suits your needs. Remember that in Java a List is an abstract, not a concrete data type. You should declare the strings as a List, and then initialize it using the ArrayList implementation.

List<String> strings = new ArrayList<String>();

This separation of Abstract Data Type and specific implementation is one the key aspects of object oriented programming.

An ArrayList implements the List Abstract Data Type using an array as its underlying implementation. Access speed is virtually identical to an array, with the additional advantages of being able to add and subtract elements to a List (although this is an O(n) operation with an ArrayList) and that if you decide to change the underlying implementation later on you can. For example, if you realize you need synchronized access, you can change the implementation to a Vector without rewriting all your code.

In fact, the ArrayList was specifically designed to replace the low-level array construct in most contexts. If Java was being designed today, it's entirely possible that arrays would have been left out altogether in favor of the ArrayList construct.

Since arrays keep all the data in a contiguous chunk of memory (unlike Lists), would the use of an array to store thousands of strings cause problems ?

In Java, all collections store only references to objects, not the objects themselves. Both arrays and ArrayList will store a few thousand references in a contiguous array, so they are essentially identical. You can consider that a contiguous block of a few thousand 32-bit references will always be readily available on modern hardware. This does not guarantee that you will not run out of memory altogether, of course, just that the contiguous block of memory requirement is not difficult to fufil.