A simple model of the term structure of interest rates is introduced in which the family of instantaneous forward rates evolves as a continuous Gaussian random field. A necessary and sufficient condition for the associated family of discounted zero-coupon bond prices to be martingales is given, permitting the consistent pricing of interest rate'contingent claims. Examples of the pricing of interest-rate caps and the situation when the Gaussian random field may be viewed as a deterministic time change of the standard Brownian sheet are discussed