On the shady wall of a Graves Ave., Encino, CA, house all afternoon. Thanks to berkshirenaturalist for helping me ID this one (said it was a female) and providing the following:

On Wikipedia:
Stagmomantis limbata, common name "bordered mantis" or "Arizona mantis," is a species of praying mantis native to North America. This beneficial insect is green or beige in color and grows up to around 3 inches long.

Description

S. limbata is a moderately large mantid. The facial plate (below and between antennae) is about twice as wide as it is long, typical of the genus, though the eyes are not as protruding as the Carolina Mantid's. Females are most often fairly plain green (often with a yellowish abdomen), but sometimes gray, or light brown, with dark spot in middle of the tegmina, which do not completely cover the wide abdomen. Hind wings may be checkered or striped yellow.

Males are slender, long-winged, and variable in color, but most often green and brown with the sides of the folded tegmina green and top brownish (may be solid gray, brown, green, or any combination of these). Abdomen without prominent dark spots on top. The wings are transparent, usually with cloudy brownish spots on outer half.

Habitat

Variable, often in open semi-arid areas in tall forbs, shrubs, or trees, but more abundant in lusher, often riparian and wooded areas of streamsides, roadsides, canyons, in towns, etc.

Range

Texas to Southern California, north into Colorado and Utah, south into Mexico.