Short answer: you have to ensure the thread-safety by yourself.
The readonly
keyword on a field gives you the insurance that the field cannot be modified after the object containing this field has been constructed.
So the only write you can have for this field is contained in the constructor (or in the field initialization), and a read through a method call cannot occur before the object is constructed, hence the thread-safety of readonly
.
If you want to implement caching, you break the assumption that only one write occurs (since "caching writes" can and will occur during you reads), and thus there can be threading problems in bad cases (think you're reading lines from a file, two threads can call the find method with the same parameter but read two different lines and therefore get different results). What you want to implement is observational immutability. This related question about memoization may help you with an elegant answer.