A major obstacle in understanding the mechanism of Cooper pairing in the cuprates is the existence of various intertwined orders associated with spin, charge, and Cooper pairs. Of particular importance is the ubiquitous charge order features that have been observed in a variety of cuprates, especially in the underdoped regime of the phase diagram. To explain the origin of the charge order and its implication to the superconducting phase, many theoretical models have been proposed, such as charge stripes, electronic nematicity, and Fermi surface instability. A highly appealing physical picture is the so-called pair density wave (PDW), a periodic modulation of Cooper paring in space, which may also induce a charge order. To elucidate the existence and nature of the PDW order, here we use scanning tunneling microscopy (STM) to investigate a severely underdoped Bi2Sr2CaCu2O8+{delta}, in which superconductivity just emerges on top of a pronounced checkerboard charge order. By analyzing the spatial distribution of the spectral features characteristic of superconductivity, we observe a periodic modulation of both the superconducting coherence peak and gap depth, demonstrating the existence of a density wave order of Cooper pairing. The PDW order has the same spatial periodicity as the charge order, and the amplitudes of the two orders exhibit clear positive correlation. These results shed important new lights on the origin of and interplay between the charge order and Cooper pairing modulation in the cuprates.
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