Using 80 years of patent-level data, we show that unlisted firms are "quietly ahead" of stock market–listed firms in the innovation race. While unlisted firms produced less valuable innovations for much of the twentieth century, they have risen to a leading position in innovation value this century. This reversal is not explained by changes in patent characteristics or by shifts in market multiples applied to those characteristics. Instead, it reflects differences in technology-field allocation: beginning in the 1980s, unlisted firms reallocated R&D toward fields with rising market valuations and away from declining ones. A simple conceptual lens highlights how nimble reallocation toward high-value fields becomes more valuable as technological opportunities grow more dispersed and persistent. Unlisted firms---especially young and first-time patenters---adjust more nimbly to emerging value signals, aided by venture capital. As a result, their share of aggregate R&D value-add has more than tripled since 1985, despite stable patent shares and faster R&D spending growth among listed firms.